Posted: 05/06/2012 at 12:58
You have several options really. Since its flowering in May/ June, its almost certainly Group 2. Large flowered hybrids that flower twice a year, right now on last year's growth and a second flush of smaller/single flowers in late summer on any new growth this year.
Usually, these Clematis require little pruning but yours needs better support so cutting it back will not kill it per se, it will just have some extra growing to do and there will be loss of flower. If you prune now, you will lose the second flush of flowers in late summer + next years, since buds are made on new growth this year.
If you prune late summer, you will only lose its big flowers for May/June, but it will undoubtedly send up new shoots in spring and may pop out a few small blooms by the end of next summer.
Don't forget to feed it in spring.