Tomato-tone by Espoma. Clematis love it. I just dump a handful at the base of each plant every few weeks and water.

Clematis should do well on any tomato or rose fertilizer. Since I also grow roses, I use whatever rose fertilizer I have on hand at the time. In the past I've used Espoma Rose-Tone, Mills Magic Mix, Dr. Earth, etc.... on my clematis and they have always done well. I also will give them a couple applications of seaweed and/or fish emulsion over the course of the growing season. Not to mention a bit of alfalf tea also.

The responses you get here will vary from poster to poster. There is not just one perfect fertilizer for clematis. I personally have never used tomato or rose fertilizer on any of my clematis just because I have never purchased it since I don't grow roses and have never had the need for a specific fertilizer for any plant I have grown.

I tend to use what is available at the time and have used generic slow release fertilizer, Miracle Grow, alfalfa tea, compost, composted cow manure, fish emulsion, grass clippings, etc. The only recommendation that I can offer is not to use an immediate release high nitrogen fertilizer since it can burn the plant if too much is applied at one time and can cause a lot of vegetative growth and fewer flowers.