The have guided tours to Pripiat' in Ukraine and I was seriously considering going but the asking price was over my budget. ( I think it was something like 300$ per person)
I'm not too sure because I've only heard stories from people who's friends went. So my information is probably not 100% reliable. From what I hear, the guides have radiation detectors and they know the paths with the less radiation. You have to follow behind them and you're not allowed to go roam about by yourself. From what I hear, they scan everybody for radiation at the exit. They ask you to bring an extra set of clothes that they leave in the car. I'm not sure if they make everyone leave their clothes behind or if they do that only if they detect some radiation on you. Apparently, a friend's friend snuck away from the group to take some pictures but the guides destroyed his gear at the exit (no sure how true that is). I'm sure they take some precautions but i don't know exactly what they are. I bet it's different from tour to tour and it's not even so strict most of the time.