All but the vigorous montana clematis are very suited to growing in containers. The pot size is important - the more vigorous the clematis, the larger is the pot needed. Because clematis are relatively light plants the support required is not complicated. From a simple wigwam shape formed from three bamboo canes to a more ornate globe of wire mesh - all are suitable.

For maximum benefit choose long-flowering varieties that are not too vigorous. The following clematis are particularly good in containers:-

Niobe - an early large-flowering hybrid.  The flowers are deep purple and look like velvet. These clematis should be lightly pruned in very early spring, but if some of the stems are hard pruned to 30cm (1ft), the flowering period will be extended by a month or so.

Clematis florida 'Seiboldii' - a stunner for container growing. It's bright flowers are put to best effect when grown against a dark background such as a wall.

This clematis is a mid to late summer flowering variety which requires only minimal pruning. Container grown it will reach a height of about 2m (6ft).

Perle D'azur is a large-flowered clematis hybrid which produces its flowers in late summer. The sky blue flowers are delicate but produced freely - it is one of the best clematis hybrids of all times.
Cut it right back to 30cm (1ft) in early Spring and it will reach a height of about 2m (6ft) in a container by the end of the season.

I have three trelis planters and I planted a clematis is each of them. After a couple of years I was unable to plant anything in the planters because of the roots from the clematis. It took a lot of work to dig them out so I won't make that mistake again.