I haven't had a lot of luck with geraniums, but Rosanne has blue blooms and does bloom most of the summer. It doesn't bloom a lot in July & August, but picks up again in the fall.
I have started substituting torenia for blue blooms. It might be an annual, but it blooms a purply blue all summer and the heat doesn't get to it.

If cultivated geraniums act here the way wild geranium grows, you will not have geraniums past the middle of May. They just die off like an annual because, yes, of the heat and humidity.

I sometimes let a few wild geraniums grow in a rich bed until they start blooming, which they're doing now, because they've interestingly shaped leaves and are mounds of green until the later plants come along. I yank them before they form those little cranebill seeds.

Nell

Hmm, guess I'll give up on this one. Nepeta Walker's Low isn't low enough; dianthus and lamb's ear are too low; I do have balloon flower but keep losing track of them so it's a miracle when some do show up every year; and I can't bear the thought of annuals - too much work! I'm afraid daylilies will be too rambunctious and compete with the roses for food. Out of ideas, for the moment.

Perennial Salvia? I'm planting Mexican Bush sage with some of my roses, it stays low most of the summer and can be kept cut back so it doesn't get so tall in the fall. Pineapple Sage is good, too, pinched back. Salvia farinacea? Boo'ful blues.

Stokesia? I've seen people complaining about Stokesia. The trick is to dead head back to a joint for a second round of blooms and then deadhead the entire bloom stem.

Rose Campion? It seeds about but isn't a pest.

Sweet William is a nicer height dianthus than the cheddar pinks.

Nell

Elisabeth, don't give up on the hardy geraniums. I wouldn't suggest planting any next to your roses because the roses will need WAY more sun, but there really are some GREAT hardy geraniums that do well here in shade.

One of the other threads has been talking about what a great groundcover veronica Georgia Blue is. If I understand what they're saying, the bloom will be gone by the time the roses bloom, but it makes a beautiful foliage groundcover the rest of the season. Nepeta subsessilus is a really low groundcover, beautiful blue blooms - although I think it blooms after rose season. Don't know much about roses, so I'm not sure. Beautiful pure blue flowers.

I grow pratia. It's in part-sun and has tiny blue flowers. VERY VERY low growing, right along the ground.
There is blue eyed grass
my own lower growing salvias and veronicas (which flop so they are more of a creeping habit here, with humidity) do not flower in the heat of summer.
The biggest problem with "blues" here is one of them seem to like heat.
You may also consider mixing plants. I grow things like golden oregano mixed with blue spruce sedum. It makes the sedum look bluer, and you can also underplant with little bulbs, blue eyed grasses etc. It would look very pretty with the georgia blue when it blooms.

GGG