Climbers need a fair depth of soil, but if you use, say, the smaller Clematis, such as The President, you'll need pots which are 2 feet deep and 12 inches wide as a minimum. Larger climbers such as Jasmine officinale need much more root room. Remember that most climbers need something to climb up - clematis needs thin supports to cling to, such as clematis netting, other climbers twine and need something to twine around. clematis also like their roots in shade, so something that shades the pots in full sun will be necessary.