I saw a video on youtube about starting cuttings from a clematis. They cut a 3' vine, removed the flowers and the growing tip. Then they cut below each node (or above each leaf pair, if its easier to understand), dipped each new stem in rooting hormone, planted it in 4" pots using a good potting soil and slid the whole thing into a clear plastic bag and stored it in the shade. I don't really remember how long they said it would take but you could tell if you see new growth. Plant them in the fall.
I plan on trying this as soon as I can find a vine with no flowers.