"Hittite hasawa: priestess, therapist, healer, diviner, and midwife," by Judith Starkton, 2011

This article has some hard-to-find information on the hasawa, which you'll usually see translated as "Old Woman" or even "sorceress," but literally means "she of birth." So midwifery, and the portals between life and death, is at the core of her power. She begins by quoting Trevor Bryce:

At all events the women so designated were multi-skilled professionals who may often have collaborated with doctors, augurs, incantation priests, and other practitioners in the arts of ritual performance, healing, and divination. As was the case with scribes, many may have been continuing a family tradition, inheriting an occupation which in some cases at least appears to have been passed down through successive generations of the same family. The names of fourteen of these women have survived, as authors of rituals which they practiced. The women in general were almost certainly literate, and may well have been multilingual to a greater or lesser degree. …

I don't see that he has evidence for this presumption, which he doubles down on in his speculation that the priestesses could not have had such a rich repertoire of litanies and rites without access to written references. In fact societies with developed oral traditions do have prodigious bodies of knowledge that is passed down without writing: the Māori and Hawaiian geneologies, the druid teachings in Britain, Gaul and Ireland; the complex chants of the Navajo; the griots and Ifa priesthoods of West Africa, to name just a few

Even at the humblest level rituals were complicated affairs, given all the paraphernalia required for their successful accomplishment, including foodstuffs and other consumable items of clay, wax, tallow, and wool, animals for sacrifice, and a range of ritual instruments. The slightest error could invalidate the whole procedure. Ritual texts … have the appearance of step-by-step instruction manuals, for careful consultation by the practitioner at every stage of the process—the collection of all the materials required for the ritual, their conveyance to the place where the ritual was to be performed, the time of the performance, the words to be uttered, the chants to be sung, the procedures to be followed in meticulous detail. There was obviously a limit to how much the ritualists could commit to memory, even when they themselves had authored a particular ritual. And there may have been many cases where a situation arose with little or no warning. Almost certainly there was a large stock of recorded material on which they could call, to ensure that they always had something ready to hand for every conceivable occasion.” (Bryce, 201-202)

Of course I am not arguing that the hasawa could not have been literate; we just do not know. Starkton quite rightly notes that the conventional (not literal) use of "Old Woman" to translate hasawa has no documented basis either. She goes on to say,

Without the services of the hasawa, Hittites believed the human and divine worlds would be fatally out of harmony, and they would have no means to restore balance.

The hasawa attempted to bring the god back through “attraction” by laying out good food and drink and sweet honey. ... She marked the path “back home” by laying out branches and textiles stretching in all directions. She performed a variety of elaborate procedures such as sacrifices. But more important than any of these actions, she accomplished her goal primarily through her words. There was a Hittite proverb, “the tongue is the bridge”—that is, the bridge between god and mankind. She told the story of finding the missing god, appeasing him, and releasing his anger. Indeed, we have these myths preserved because they were included in the directions for her rites. The telling of the myth itself acted as magic by analogy. 

Starkton's article is the source for this bronze sistrum that so many of you were interested in during the webcast. It could be Hittite, or possibly Urartian, further to the east. An Armenia bronze shows a woman in a goddess temples holding up a sistrum.

Starkton has brought us the most detailed description of the hasawa's rites and practice that I have seen. She talks about her treatment of disharmony (referring to her as a family therapist, among other functions), who combined medicines with incantations or ritual verses. She might use physical symbols in ceremonies that banished the energetic source of conflict, for example making a model of a tongue, and disposing of it, while her words of power potentized the intended process of transformation. She summarizes one detailed ritual (they could go on for days or [not continually!] over weeks) involving one of those priestesses from Kizzuwatna, near the Syrian border and very possibly Hurrian, that I talked about in the Anatolia webcast.

“These are the words of Mastigga, the woman from Kizzuwatna: If a father and (his) son, or a husband and his wife, or a brother and (his) sister quarrel, when I reconcile them, I treat as follows:

She takes black wool and wraps it in mutton fat; tissatwa they call it. She presents it to the sacrificer [i.e. the quarreling persons who asked for this procedure] and speaks as follows: ‘Whatever thou spokest with (thy) mouth (and) tongue—see, here is tissatwa! Let it be cut out of your body these days!’ She throws the tongues into the hearth.

The Old Woman speaks as follows: “In whatever curses you indulged, let now the Sun-god turn those curses (and) tongues toward the left!’ And she throws them into the hearth.

The red wool (and) the blue wool that had been placed upon the bodies of the two sacrificers, the two figures of dough that had been placed before them, and the hands and tongues of dough that had been placed upon their heads, those the Old Woman removes. She cuts the strings off them, the Old Woman breaks the two hands and the tongues of dough to pieces.

She then waves them over them and speaks as follows: ‘Let the tongues of these [days] be cut off! Let the words of these days be cut off! And she throws them [into the hearth].

…

They drive up a (white) sheep. The Old Woman presents it to the two sacrificers and speaks as follows: ‘Here is a substitute for you, a substitute for your persons. Let that tongue and that curse stay in (its) mouth!’ They spit into its mouth.

She speaks as follows: “Spit out those evil curses!’ They dig a hole in the ground, cut the sheep up over it, and then put it into it.

They put 1 thin sacrificial loaf down with it, she also pours out a libation of wine and they level the ground.

…

She speaks as follows: ‘Let the evil words of mouth (and) tongue be rubbed away from you!” (Unal, 67-69)

This ritual use of wool, such as the twisting together of black and white cords, is also attested in Babylonian magic.

Drummer from palace of Neo-Hittite king Barektu at Zinjirli, Turkey, 8th century bce.

We cannot be certain that this is a woman; long hair is not necessarily an indicator of femaleness, nor is flat chest an indicator of maleness (not in this art style at least). There's no beard, however, which weighs toward a woman, and more importantly, the frame drum is an attribute heavily associated with women. The lack of veil points to her being either unmarried or of subaltern class, probably enslaved. The Assyrian laws heavily penalized lower class women from wearing the veil, which was a marker of class status as well as an enforcement of patriarchal modesty codes.

Hittite healers also did ceremonies to transfer pain, illness, and affliction to an animal to be carried away to untrammeled Nature. She “wraps up a small piece of tin in a bowstring and attaches it to the patients’ right hands and feet; then she takes it off again and attaches it to a mouse, saying: ‘I have taken the evil off you and attached it to this mouse. Let this mouse carry it on a long journey to the high mountains, hills and dales’”(Gurney, 50).

Or it could be sent to the Underworld, which the hasawa did in curse-removing ceremonies. Starkton describes how she would take away the disordered energy and bury it in palhi, bronze vessels sealed with lead or iron latches. (I'm quite sure that ceramics would be used this way by commoners who couldn't afford bronze or smiths, but that didn't make it into the elite written record.

Starkton continues to divination: "There were many kinds of seers and diviners in ancient Anatolia. They consulted the stars, birds, the innards of sacrificial animals, and dreams among other things. We hear of the hasawa mostly in terms of two kinds of divinations: “lot-oracles” and “snake divinations.” The lot oracle seems to have involved some kind of board with symbols drawn on it representing various aspects or activities in life (Bryce, 151) and perhaps dice, but it also lasted for multiple days, so put aside your vision of a Ouija board!

"The snakes were released into a basin filled with water and marked out in sections such as ‘life’ ‘sin’ ‘temple’ (Bryce, 151 and Frantz-Szabo, 2017). In both of these the format appears to have been a series of yes and no questions asked by the hasawa or the “sinner,” and then the answer was interpreted by the hasawa from the movement of the lots or the snakes."

This yes-or-no method is also used in many traditions using rites with a pendulum (In Europe, this was often a sieve suspended in some way, and i'll post separately about that.)

Starkton: "It is likely that the hasawa originated as a midwife. The Hittite verb “has” means “to give birth” and, indeed, the hasawa attends on women in labor as one of her duties. There are other midwife attendants in the Hittite lexicon such as “hasnupallas” which means “one who is skilled in causing to give birth” (Pringle). The texts that mention these women come from different periods, so perhaps terms changed over time. Occasionally two different attendants are present, other times the hasawa or the hasnupallas works alone. Nowhere are their duties clearly delineated. But a job description for the hasawa would include some version of midwife.

"The midwife’s duties included preparations before, during and after the birth. Presumably she had practical knowledge about delivering babies—we know she used a birthing stool for the mother and sat on a stool herself, used three pillows and a knife in the project—but what we hear about from the tablets are rites to purify and protect the mother and child. Rites were performed to purify the birth stool and wooden pegs that were bound somewhere, perhaps to the birth stool itself. “She beseeches the gods to remove evil influences and to grant a desirable fate to the child” (Beckman 1993, 38).

"The midwife recited the myth of the Moongod Armas who protected the mother of his child in her difficult delivery, another example of using myth to bring about magic by analogy. In one tablet she takes the combs used to card sheep’s wool and “combs” the body parts of the child to heal them after birth. [One of many forms of ritually removing negative energies, along with bathing, smoking with herbs, anointing the body, or wrapping with / tying on bundles with herbs, stones, or other potent substances.] There was an “Incantation of Crying Out” [for the mother in labor] and one to induce the child to leave the body of the mother. (Beckman 1983)

"The blessing which the hasawa said over the new baby is a fitting way to end an article examining the remarkable importance of this woman’s job in Hittite society. If the baby was a boy, the hasawa said, “Let a female child be born in a year forth.” [The reverse was proclaimed if the newborn was a girl.] Female children were apparently as welcome to a Hittite family as a male child (Pringle)."

Look at the link in the first post for her bibliography.