Lonicera tragophylla and Lonicera tellmaniana, IF they are hardy, will do well in shade.

You might try Japanese Honeysuckle as well; it's probably not invasive in your area. I know it grows in a protected spot in zone 5; you would probably have to mulch it.

Japanese Honeysuckle has a fragrant white flower which turns golden yellow as it ages. In warmer climates it can be invasive.

You can grow hops in part shade, but it probably won't flower. The leaves are broad and attractive, though, and if it grows too vigorously the shoots are supposed to be edible. There is a yellow variety of Monkshood (poisonous) that it might be a good backdrop for.

I planted an autumn blooming clematis (the one with hundreds of tiny white flowers) in part shade years ago; thought it had died out and went back a week or so ago to find it in bloom now, in June--but only with a few flowers, not hundreds.

Grape vines will grow in that situation, but probably not produce grapes.

You could try Russian lace vine, which can easily take out a tree, but don't plant it if you don't want it forever; it is supposed to have a deep tap root. If it gets some direct sun, it should produce bunches of tiny white flowers which look like lace from a distance. It would probably overpower a small trellis, but could easily cover a large trellis or even a gazebo.

The above all are hardy in S. Central PA; if interested in any you should doublecheck for hardiness in your area though. You are far enough north that anything would probably die back to the ground in winter, and would need fairly heavy mulching in winter.

If you can't find a suitable flowering perennial, you might want to consider planting something that would give your trellis a nice leaf cover, then add some summer annual vines in pots next to it to provide the flowers.

Speaking of grape vines, this is in the vitex family, but instead produces tiny round fruit that is purple, white, and pink, hence the name 'Porcelain Vine'. The botanical name is ampelopsis brevipedunculata. THe foliage is variegated white and green. Not invasive, but healthy growing once it is established.

Wow! You're in zone 3/4? You may have to do some research on the net to find something that is hardy in your zone.

Susan

Dropmore scarlet honeysuckle is said to do well in part shade and is hardy to zone 3. Tangeutica clematis (golden clematis) will also do well in part shade; zone 2. There is also the annual canary bird vine which grows very quickly. Good luck!