Posted: 25/03/2016 at 17:52
Rubi - there are plenty of clematis which you can grow in a container, but bear in mind that they need more attention in terms of food and water, especially during hot weather. Ideally, you want as big a container as possible, and you'll need something to attach them to - trellis, or even just wires on vine eyes since you have a fence. Then you can arrange the new growth horizontally to give more coverage, rather than just letting the plant grow vertically.
Take a look at Taylor's Clematis site and you'll find lots of choices suitable for that aspect, and also ones which are happy in pots