Dig wide and deep and don't be surprised if they seperate into many smaller clematis plants. That happened to one of mine when I decided to move it. Also I suggest you cut the vines back before moving as they will need to be cut back anyway to help roots get re-established.

Thank you, mnwsgal. Sounds doable. It will be too hot for a few days, but next week should be good. I have a lot of clematis, but I don't do much for them except prune according to which group they're in and feed them once in a while. This will be my first attempt at moving one.