Buy clems that don't grow as tall.

Here are some suggestions

http://simplyclems.com/

I agree with Janet..buy varieties that only get to a certain height to fit your requirement..you can also use COTW and the search function by putting in desired height,color,pruning group etc to narrow it down to your specific desires.
It isn't uncommon for some clematis to just "sit" & "rest" after pinching in their first year..that is why they say they SLEEP the first year..I find this more common with some pruning group 2's than 3's but happens with all..reading and learning from people who grow clematis to which varieties are more vigorous in their gardens will help you in making those choices BUT if you heart just sings when you see a pic of a clematis that is a "must have" then you will gladly suffer through that "Sleep" & "Creep" period to enjoy the "Leap" & thereafter years..I know it truly has been worth the wait for me..I find continuous planting year after year gives me a thrill with that year being the "leap" year of some while planting dreams of whats to come in future years..but then again..I fear that is a convoluted expression only resulting from my addiction!!..Plant & pinch away for future pleasure...Jeanne

Thanks for the responses, and I'd still like to know if it's feasible to train clems horizontally and if it's possible to limit their height. I've been researching shorter ones, but the ones I really really want happen to be taller.

You really have to be determined to train a clematis horizontally. I trained a Montana Reubens along my fence but it meant going by every day and wrapping the ends around the wire or using twist ties to hold them.

{{gwi:577849}}

I have lots that grow too tall for their supports, and often use strings tied to a higher place and try to get the clems to follow this path. Yes, it does take a lot of fussing and tying, but I think this is one of my joys to play with the vines. I seem to like long vines rather than short busy ones.

Marie

I meant bushy, not busy