In my experience planting near Boxwoods is problematic, they out compete the Clematis for water. I tried to enhance a hedge with them but all but one dwindled away. Nothing thrives very close to the hedge. It is going to depend on how close to the boxwood and how much hand watering you want to do. Clems don't deal well with root competition. Height of all of them varies. Most outgrow their tags for me, your situation may be different since you are colder. You can't really count on published heights. They will flop back down if they don't have a place to keep going. They climb wire much easier than wood as far as trellises go. All take three years or so to establish.

My clematis grow as tall as their support and then work their way sideways or flip down as well, but mine don't generally seem to get larger than their published height. I am not sure this is a good spot for clematis since you have a quite narrow actual planting space between the root competition from the boxwoods and the rain shadow caused by the building. If you have eaves, the area rain doesn't reach will be wider, but even a building without eaves will create some.

I think if you want to do this you will want to have regular irrigation for both the boxwoods and the clematis, and even then I don't know about the success. Or do you have space for a couple of really large pots? If you choose the hardiest varieties and a bit of insulation in winter, they could probably survive in large pots outdoors year round.

IME boxwoods will get larger eventually, and whoever planted these may have done so with the plants' larger size in mind. I might consider planting something that is more tolerant of dry soil such as tall dahlias (which would need to be dug up and stored or replanted annually or perhaps annual vines in pots while waiting for the boxwoods to get larger.

If you add a photo of the spot, you may get other suggestions.