Ever since reading about the Salem witch trials I've been fascinated with the idea. (Last night my wife and I were watching heretics being burned on The Tudors, which is what brought the topic to mind.)
For the sake of discussion, a definition: a witch is a woman with a connection to evil supernatural beings that grant her the power to afflict others with sickness, death, and misfortune without leaving any tangible evidence.
So let's set aside the question of whether or not there were or are real witches. Hypothetically, what would you do if you believed there were, and if you thought someone was a witch?
If someone were hurting others and it could be proven with tangible evidence, then you'd use that evidence in court to charge, convict, and sentence her according to law.
But if the person you believed to be causing the illegal harm were doing it via witchcraft -- and therefore leaving no tangible evidence -- what do you do? I can only see two options.
1. You appease the witch. There's no tangible evidence, and you won't act outside the law. The witch runs free, afflicting and extorting anyone she desires. (And remember, we're assuming she really is a witch.) Give her what she wants and maybe she'll go away (or at least bother someone else).
2. In collaboration with your fellow citizens -- who are all threatened by the witch -- you create some sort of extra-judicial proceeding designed to discover and neutralize the witch. You're very interested in justice, but since the crimes are being committed by witchcraft that leaves no tangible evidence your judgment will have to rely on testimony by witnesses. These witnesses will testify about what they've seen the witch do, and about her character. (Character is especially relevant since the witch derives her powers from evil supernatural beings.)
In modern times such circumstantial evidence is often used to convict criminals even when there is scant tangible physical evidence. People have been convicted of murder without even a dead body in evidence! So maybe your proceedings wouldn't even have to be that far outside the law.
Choice (3) is basically what the citizens of Salem chose to do. It's hard for me to argue that I'd have done any different, if I had been in their place.