There is a lovely evergreen clematis, I think it is clematis armandii. It has very pretty long, green leaves and wonderful scented white flowers in the summer.
Edited to add, there are other cultivars of Clematis armandii, some with pink flowers. Here's the link to the plant database if you'd like to see pictures of it.
Clematis (Clematis armandii)
Other clematis are lovely, but would not be evergreen.
