What is the word for the study of witches and witchcraft?

"Witchcraft Studies"

See for example "A Neglected Aspect of Witchcraft Studies", "Witchcraft studies in Austria, Germany and Switzerland" and "Witchcraft Studies from the Perspective of Women’s and Gender History: A Report on Recent Research".

The term has been used for the study of modern practices of witchcraft like Wicca, Feri, 1734, etc. for the study of earlier practices these have sometimes claimed to descend from (including a range of positions as to whether that is the case) for the beliefs of those who claimed that witches were attacking society (from the witch crazes of the early modern period and earlier through to the "Satanic Panic" of the 1980s and beyond) and to other practices of magic that have been given the label "witchcraft". It has also been used for historical, sociological, political and other analyses of witchcraft.

As such it fits your question very well.

It's wide enough that you may wish to be narrower as with something like "history of witchcraft" etc.

It also overlaps with "pagan studies", in that something covering modern pagan witchcraft like Hutton's Triumph of the Moon or Joanne Pearson's Wicca and the Christian Heritage would definitely be in the overlap, something like Margot Adler's Drawing Down the Moon would be more "pagan studies" than "witchcraft studies" as while it is certainly significant in the latter it covers much in the wider scope, and something like Levack's The Witch-Hunt in Early Modern Europe would be "witchcraft studies" but not directly concerned with "pagan studies" as it doesn't look at modern witchcraft practices at all and as such is only relevant to actual witchcraft practices and (by extension) paganism in so far as the period it studies has a cultural significance among modern witches.

English-speaking academics in the humanities don't use -ology or -ics constructions much to distinguish what they do from what their colleagues in the same field or 'neighbouring' fields do: those suffixes designate disciplines rather than topics.

Topics are usually designated with the word studies, either following the name of the topic, if that is short—Shakespeare studies, Carolingian studies, textual studies—or followed by in + topic name if that is longer—studies in mediaeval pilgrimage, studies in 17th-century verse. I'd go with

Witchcraft studies ... or, if you need a book or seminar title,
Studies in Witchcraft, Benjamin, Spring semester 2015.

I nominate a neologism: wikkology

wikkology — The study of witches; the study of the practicing of witchcraft. cf. demonology

It is reasonably derived from some of the etymological sources for witch: https://en.wiktionary.org/wiki/witch

It fills the need for a concise -ology form, and should not be controversial in any way.

This question has bothered me for many years, and is exacerbated each time I peruse a favorite book of mine, The Encyclopedia of Witchcraft & Demonology by Rossell Hope Robbins. In fact, I came here to pose this question, and discovered that a discussion was already underway. I formulated the neologism several months ago in a fit of determination but haven't been afforded an opportunity to use it. Since it seems there is no consensus about the existence of an accepted term, I offer wikkology to the world, and time will tell if it gains any traction.