Clematis - Montana and Elsa Spath

C. montana do not normally need any pruning, except to remove dead gorwth or where it has overrun its alloted space. C. Elsa Spath is a Group 2 Cleamtis for pruning, so basically that also does not need anything other than remedial pruning. If either is pruned it should be in late spring.
If they are both young plants then you could possibly get away with gently untangling them from the trellis, but Clematis soft growth is very brittle. If you are going to prune then do it now so you get new growth over the Summer. Feed with a good general fertiliser after severe pruning by the way.

The montana you can prune after flowering, as next years flowers will grow on this years growth.
Group 1.

Elsa Spath is a group 2 and it says in my book to prune before flowering in early spring to strong buds as this is where new shoots will grow and flower in the summer.

I hope this helps.

P.S.
I drilled holes in my wall and then tied my trellis on with wire so, that when it comes to painting etc I only have to un twist the wire and lift the trellis down..

And just to confuse you even more,both of the above answers are accurate! Prune Group 2 means no pruning, so Elsa Spath doesn't need it, but if you want to limit its growth, prune in the winter (by 15th February). Doing this means you will sacrifice the larger, early flowers, but you will still get the later crop of smaller ones.

thanks all for bril answers - got some delicate work cut out this weekend I think