I have moved clematis and still had blooms though the bloom time might not last as long the first year it's transplanted.

Take as much of the root mass as you can - try for 15-18" across. It's going to be very heavy, so you will need a good back or get a helper with a good back. Have your hole ready. I generally stick a couple of bamboo sticks around the root ball to help support and keep the vines upright. When I'm moving it, I let the bamboo with the vines tied to it rest on my shoulder. I always feel like super woman when I successfully move a clematis without cutting it back or breaking a stem :)

Keep it water well, but be careful to water so much that the soil stays soggy.

It might get very sulky if it gets hot and dry this summer. It will usually rebound during the evening or when in shade, but if it doesn't rebound, then it's a good idea to cut it back.