They are heavy feeders, like roses.
I feed mine Espoma Rose Tone and top dress with compost. I usually feed them once a month in the summer season, but only put compost on them early in the season.
Hope this helps!

I've already tossed all of mine a few handfuls of alfalfa pellets and they were composted last fall. I'll use Rose Tone too when I get around to it.

Alfalfa pellets are horse feed and cheap at feed stores. Very cheap, organic and easy.

I'm not at all sure I'd agree they are heavy feeders. In my previous garden, I had scores of clematis planted that never received routine fertilization and they flourished and bloomed prolifically. I did mulch pretty regularly with compost and treated newly planted vines with a dose of recycled alfalfa, courtesy of my pet rabbits :-) Mulching with decent compost on at least an annual basis can eliminate the need for a lot of unnecessary fertilizing, but it does depend on the fertility of your soil to begin with.

If you feel the need to fertilize, any all purpose (all 3 numbers the same) fertilizer will work and both tomato and rose fertilizer formulations are recommended for clems. I'd prefer to go with a granulated organic type, worked lightly into the soil at pruning time or in early spring as new growth commences. Once a season is more than sufficient.

I have a lot of competing tree roots in much of my garden (neighbor's mature conifers, nothing I can do about them) and I find that I must fertilize and water everything more than if I didn't have the tree problem.

I find I not only have to fertilize twice a year, I actually replace all of the dirt around the clematis down at least 8+ inches with compost - at least every other year.

Katie