This is a very vigorous type of Clematis that wouldn't be happy in a pot for very long. There are a lot of Clematis being bred to grow in pots, I suggest that you buy one of those instead.

Clematis montana, no, but others can be - as mentioned above, there are a few smaller hybrids coming out, but even so, some of the ordinary ones will grow in pots, but the pots need to be a minimum of 2 feet deep and 12 inches wide. Even then, the clematis won't achieve the height and spread it would in the ground - choose a variety that reaches 8 to 10 feet max for a pot, such as The President or Niobe, for instance.

And - if you do grow a Clematis in a pot, you have to make sure that the roots are cool, so either plant additional plants in with it to shade them, or add a topping of pebbles.

C montana definitely wont survive in a pot - it is a thug of a Clematis and lord knows how far its roots go down in our garden! As has already been said there are Clematis designed for pots but do shade the roots or your plant will not be happy. The C montana on a west facing wall of our huge potting shed that gets little sun due to house grows like a weed, flowers like mad and is pruned several times a year to prevent it taking over the roof of said shed.