I have posted occasionally on the question of female Jewish scribes. Go here and follow the links. The earliest soferet I know of is Hannah bat Menahem Zion in the thirteenth century, noted by Hebrew-manuscript expert Collette Sirat. (Via Aviel Barclay-Rothschild, modern soferet-blogger.) Barclay-Rothschild also quotes a note by an anonymous female scribe who seeks indulgence for any errors in her work, because she was distracted during it by having a baby. Sirat refers to "fewer than ten" named medieval female scribes, while Manuscript Boy comes up with more than twenty "pre-modern" ones at Hagahot. These posts were back in 2004-5, and I imagine the question has advanced since then.
I am especially curious about evidence for female scribes in antiquity (say, before 600 C.E.) in any manuscript tradition in the Middle East or Europe. I don't know of any, but I haven't made any serious effort to look. If you have information, please drop me a note so I can share it.
UPDATE: Reader Michael Lyons refers me to Kim Haines-Eitzen, "Girls Trained in Beautiful Writing": Female Scribes in Roman Antiquity and Early Christianity." Journal of Early Christian Studies, Volume 6, Number 4, Winter 1998, pp. 629-646. The full text of the article is available at the link through Project Muse, but it's behind a subscription wall. The article's launching point is Eusebius' Ecclesiastical History 6.23.1-2, but it touches on ancient Near Eastern evidence and surveys evidence from Greco-Roman and Christian monastic literature. The passage by Eusebius reads:
1. At that time Origen began his commentaries on the Divine Scriptures, being urged thereto by Ambrose, who employed innumerable incentives, not only exhorting him by word, but also furnishing abundant means.(Translation by Arthur Cushman McGiffert, Nicene and Post-Nicene Fathers, Second Series, Vol. 1.)
2. For he dictated to more than seven amanuenses, who relieved each other at appointed times. And he employed no fewer copyists, besides girls who were skilled in elegant writing. For all these Ambrose furnished the necessary expense in abundance, manifesting himself an inexpressible earnestness in diligence and zeal for the divine oracles, by which he especially pressed him on to the preparation of his commentaries.
UPDATE: Mladen Popovic e-mails to alert us to Haines-Eitzen's more recent book, The Gendered Palimpsest: Women, Writing, and Representation in Early Christianity (OUP, 2011).