I would suggest a Jackmanii (deep purple) or Polish Spirit. You can even try Prince Charles or some other blue cultivar. Stay away from white or pinks in the hot summer on this wall as they will fade and droop

I think Price Charles would be gorgeous with that rose. I have mine planted with Rouge Cardinal which is a similar color and love it.

If you are wanting a white clematis to bloom when your rose isn't then you don't want an early blooming ..you want a later blooming clematis and the viticellas would fit the bill..I would suggest either "Huldine" or "John Huxtable"..they are pruning group 3's...Now your Pruning group 2's would bloom about now in your zone and again in late summer/early fall...If it's a two that you want then either "Snow Queen" or "Guernsey Cream" would look fantastic....Jeanne

What I want is a white clematis that will bloom with the rose and another that will bloom after the rose and the white clem are done. Or just one for after the rose is done.

I have John Huxtable in another area and it is blooming now. I like it but it blooms too late to go with 'Night Owl'. I also have 'Polish Spirit' paired with the rose 'Awakening' and I like it alot. I could do something like it for the later bloomer. I think I have to go with a group 2 if I want an early bloomer to go with the rose bloom time. In that case I checked out a couple of websites and these might work:

Duchesse of Edinburgh
Matka Siedliska
Snow Queen
Anna Karolina
Matka Teresa
Sylvia Denny

Unfortunately, Guernsey Cream doesn't like that much sun so it doesn't go on the list.

Then for the late blooming clematis from group 2 I'd like something in the darker pink/reds like Warsaw Nike.

I think I need to stick to group 2s for both of them to make pruning them easier if I go with two. I know most rose growers like to use group 3s with their climbers so they can prune them down when they prune the roses. If I give up on the idea to use an early bloomer with the rose then I can go with a group 3 for the summer show. In which case the choices could be:

Abundance
Brocade
Mme Julia Correvon
Polonez
Royal Velours
Slowianka

Does anyone grow these? Are they good choices?

I ordered this from Bluestone Perennials, Lanuginosa Candida about 3 years back, its is absolutely beautiful and blooms from spring til fall for me. Do a search at Bluestone to see it.
Alberta

I have been looking at whites myself and although I don't grow any at the moment, try looking up "jerzy Popieluszko" on Clematis on the Web. It is an award winning clem that blooms profusely and appears to be considered an early flowering clem but continues profusely.
The other one that appears to flower early is "Toki" the yellow anthers may really look nice with the yellow centres of your rose. Again, I don't grow either and don't know much about them but thought they seem to fit your requirements. Best of luck!

Just a follow up, I picked up Snow Queen and will be looking for a pink/red that will bloom later. Snow Queen has two blooms on her and I love the purple centers.

You will love "SnowQueen"..isn't she grand..I just love this clematis and such a vigorous bloomer!!..Jeanne

Marie Boiselotte(sp?) has been a good one for me.