I have a lot of mildew in my garden this year too, especially on several of my roses. I would think you could spray your clematis with the cornell formula (baking soda, hort oil and water) or Safer's Defender (a prepared sulphur-based fungicide). As far as I know, they wouldn't damage your clems. Perhaps someone who has tried these methods will comment on their effectiveness. I have also heard of hosing the affected plants down early in the morning on a sunny day and letting them dry off. (Of course, you would spray the fungicides AFTER you did that:)) It's supposed to 'wash off' the spores.
Judith

I'm getting rid of some that mildew every year. I just don't have time to spray. I never had mildew until I introduced some viticellas and texensis.....