Growing clematis in containers is not only attractive; it is sometimes essential. Terraces, patios, balconies, roof gardens are all places where deep cultivation outside a pot is impossible. There are also parts of the country where because of poor drainage or a high water table the soil is simply unsuitable. If there is one thing that clematis demand it is good drainage.
Ideally the container you use should offer as much protection as possible against hot conditions. Materials that conduct heat slowly such as thick pottery, stone or wood are preferable to cheap plastic and (really) expensive lead. Light colours are better than dark. Ideally you should position the container where it is out of the worst of the sun.
Most containers have plenty of drainage, but I find as a rule that the prettier the pot, the fewer holes it has. If it is a workable material, enlarge or drill more, if it is not workable, don't use it. In a perfect world, the container you use should also be held just off the ground. If it sits flush, the drainage holes can get blocked and the plant suffers.
Container size is important as clematis have large, greedy roots. Smaller varieties will survive in a small pot, but flowering will be poor and they will be disease prone.
Give your clematis a proper home - a good sized container will be at least 15 inches (40cms) wide and 18" (45cms) deep. These measurements are the minimum and apply to the smallest dimension. So if the pot is narrower at the base than the top, then it is the width at the base that matters.
Compost for growing clematis in containers is important. For all sorts of reasons try to stay away from peat based (i.e. composts where peat is the main constituent). Apart from being ecologically unsound, it is almost impossible to wetten once dry and it has virtually no nutrient content in its own right. Don't use garden soil either as it will no thave the food or balance necessary and generally performs very badly in posts.
Although it is heavier and more expensive per litre than peat-based composts, there really is no substitute for John Innes No. 3. This is a soil-based compost (it only contains a small amount of peat) and so it is easy to water, has excellent drainage and contains the slow release nutrients necessary for keeping a plant that will be in it for a very long time in good condition.
Supporting container grown clematis is probably a topic for a book... but whatever you use, remember that clematis climb. They carry a considerable amount of foliage and so act like a sail. If the support is not strong enough and well anchored, it will break and damage your plant.
Sticks in the container tend not to be a good idea as they wave in the breeze and cause wind rock. My container grown clematis are all Group 3 (or C). These are clematis that flower on the growth of the current year. They have the advantage that they are pruned back to 12-18" above soil level every year in late winter. This means their supports can be replaced or repaired as necessary and the plant can be moved around to different locations. Hard to do with a Montana...
Maintenance of container grown clematis involves ensuring they are well watered through the growing season. A clematis that dries out will not forgive you in a hurry (if at all).
You can feed your clematis while watering. Every fortnight, use a liquid feed (root and foliar) such as Liquid Growmore which contains equal parts of nitrogen (N) and potash (K). All fertilisers list their makeup on the label. Use one with equal parts of N and K. Start feeding as the plant breaks into growth but stop as soon as you see a flower bud. Then do not feed again until flowering has stopped.
If flowering continues into early autumn, don't feed until the following spring. Too much feed, too late in the season encourages soft growth which will be killed by frost. And your clematis in a pot is pruned in exactly the same way and at the same time as the same variety grown in the soil.