Do cessationists perform exorcisms?

This is actually a very difficult question. The answer is some do and some do not and that by in large the subject is not written about and is more of a pastor to pastor situation.

The reason I say it’s difficult is that its a little difficult to say who is a cessestionist exactly and then among those famous leaders in that group, what is their position on modern day exorcism. To make matters more complicated, the charismatic movement, that I understand is largely popularized by the Pentecostal movement in the Azusa Street Revival has had its impact on all Protestant groups and even Catholic groups blurring the boundary lines even within denominations.

The way I think of it is more historical and steady state with the cessationist path more or less being: Luther and Calvin, John Owen and Jonathan Edwards (maybe throw in Whitefield and Wesley in as well for some big names) finally tracing a kind of slight split on the topic of Revival among more modern evangelical theologians, like Dr. Martin Lloyd Jones (a more charismatic and impressive speaker who is still of the Owens, Edwards theological vein) and J. I. Packer (more strictly speaking true to Owen’s outlines yet not that impressive as a speaker in term of powerful effect). Interestingly, both people, Lloyd Jones and Packer do not deny modern day exorcism, but Lloyd Jones actually did it as part of his pastoral job.

Luther/Calvin accepted exorcism in a simple way, not with any of what he considered 'superstitious ceremonial ways' by Catholics, especially during baptism.

There at Arnstadt the pastor has driven a devil out of a young girl in a truly Christian way. Regarding this event we say: may the will of God, who is still alive, be done, even though the devil should be sorry about this.

Footnote: The background of this statement, esp. the identity of the pastor, could not be established. On the basis of the material presented in WA, Br 11, 33, it seems as if there was still a “papistic preacher,” at least in Greussen, but perhaps also in Arnstadt at that time. When Luther says that the pastor handled the matter “in a Christian way,” this suggests that the pastor did not use the complicated, colorful, and dramatic papal rite of exorcism, but a more simple one. For Luther’s practice of exorcism, see WA, TR 3, No. 3739. (Luther, M. (1999). Luther’s works, vol. 50: Letters III. (J. J. Pelikan, H. C. Oswald, & H. T. Lehmann, Eds.). Philadelphia: Fortress Press.)

To find any comments about exorcism that are not from the angle of suspecting devilish fakes among Owen or Edwards is difficult, although they speak very little about it. Yet both firmly believe in the demonic realm and its activity against the modern church. Edwards is central is talking about modern day revivals yet I do not see it any different than the revival during Luther's time, except that it was less impactful.

I find it very difficult to find any clear options beyond cynical ones from Owen and Edwards. Calvin also seems open to a simple exorcism. The Puritans in general seemed silent on the matter but a few practiced exorcism. I gather all the Puritans to be cessationists as the alternative views are quite recent in theological history.

Whats a little perplexing is that among all Protestants Puritans were very aware of the devil and demons and fiercely defend their existence. So it is illogical to not then assume the possibility of demonic possession. If demonic possession occurs, its illogical to avoid the topic during regeneration and redemption. It is therefore my view that throughout the centuries many demon possessed individuals experienced exorcism the moment they received the gospel, regardless of the individual belief of the local pastor. In addition Spirit filled pastors or other believers who happened to encounter someone possessed who had obvious corresponding behaviors of demonic control would practice exorcism not because it was a settled theology but because they encountered the need directly.

In conclusion, some yes, many not really.

As an interesting side note. At the age of sixteen I believe I experienced exorcism through faith, when I became a Christian by reading the Bible alone in my room. Although I have never met another Christian who experienced demonic possession prior to conversion, I am sure many exists. This makes it impossible for me to disbelieve in exorcism. I am also, as far as I know, a cessationist and ironically hope for a Spirit revival. It is really hard to finally categorize anyone and I have never considered the possibility that one particular denomination had a total monopoly on orthodoxy.