Hi I have had a confederate jasmine with a clematis on a fence, it is evergreen, beautiful scented blooms, and the clematis does well with it and blooms beautifully.
Most are only hardy to zone 8, so either plant it in a protected location (mine is close to the house and protected from winter winds), or look for a hardy variety.

HTH

Check out this web site. http://www.gardenvines.com
He is in Athens
Very reputable and has an incredible amount of Clematis,Jasmine,climbing roses, honeysuckle etc and you can even e-mail him if you have any questions. bobby

What about Pyracantha coccinea. Not really a vine but easy to espaliate over a trellis. They do have thorns but look gorgeous in mid winter.

Two native evergreen vines: Crossvine (Bignonia capreolata) and Carolina jessamine (Gelsemium sempervirens).

Madison Confederate Jasmine

One idea I have always liked is to mix a few vines. It is always fun to see blooms that seem out of place on a vine you recognize. Then you have several bloom seasons for the trellis. You could do a sturdy evergreen, and at least one or two clematis like Jackmanni and the white Autumn something. How strong and big are your structures, or are they over a walkway, and how much maintenance do you want to do? I am really crazy about vines of all kinds. Look at The Lady Banks Rose, not really a rose, no thorns, and prolific. Mine is starting to make the clusters of small yellow buds. The pyracanthas are beautiful, anfd make orange or red berries. The black-eyed Susan and the Moonflower are two of my favorite annuals, both do make seeds, you have to gather the moonflower seeds in the fall.

Consider using _Clematis armandii_, or Armand's clematis, which is an evergreen clematis valued for its beautiful foliage as well as its flowers. Here's a Floridata link you may want to look at:

http://www.floridata.com/ref/c/clem_arm.cfm

Holy smokes, people, don't recommend vines that become massive, spreading monsters!

Madison Confederate jasmine is the only one of reasonable stature someone already mentioned for the site conditions/scale the OP stated.

PS. firethorn shrubs stink when they bloom -- a blend of powdery sweetness and urine.

I don't think the original poster stated the size of the trellises, so some options are not necessarily "monsters". I have clematis Armondii and it is perfectly happy being pruned to a smaller size and growing without being a "monster". I grow MANY climbing roses that are fairly mannerly, ramblers, large shrub roses trained as climbers. They are not monsters.
Pyricantha doesn't stink to everyone, - just in the way junipers don't stink to everyone (or do Bradford pears). I find those two the STINKIEST horrible smells. One like dirty dog, the other like cat urine. But Pyricantha doesn't smell at all badly to me! Go figure!!

I appreciate all the help! I have two trellises (whatever the plural is) in front of the house on either side of a window. They are about 8' tall and about 18" wide, each. The blacked eyed susan vine I had grew on it very well - got to the top in a month and started back down. Looked nice until the winter!

That is a very small (meaning narrow) trellis, and yes, almost anything evergreen would simply eat it up! You need a much wider trellis, and in most cases taller than what you have. I would consider a vine that has a pretty feature in the winter such as a clematis that has pretty, fluffy seed heads for winter interest. Parusing through the Brushwood vines nursery catalog might be helpful

Here is a link that might be useful: Brushwood

Dear organic_gardenhag 10,
"Rose is a rose is a rose," is a quotation attributed to Gertrude Stein. I'm going to modify that quotation by saying, "The Lady Banks rose is a rose is a rose," its Latin name being _Rosa banksiae_. As you said, it's virtually thornless and is evergreen; however, it is as much a rose as its thorniest cousins.

With a profusion of beautiful white single, golden-centered flowers, the evergreen Cherokee Rose, Georgia's state flower, would be an excellent trellis-choice. Blooming during azalea season, the Cherokee Rose is native to China. It's thorny as all get-out and, thus, would be an excellent deterrent to cat burglars, home invaders, and other vermin. During the Antebellum Era, planters and yeoman farmers used the Cherokee Rose as natural, impenetrable fencing to keep rogue livestock confined to the pasture.