What kind of clematis do you have? I just use chicken wire or a trellis to get my clematis climbing up to where I want it, then weave the clematis across the top of the fencing. I'll leave a pic of my fence/clematis.

This is just a 4' picket fence. Sweet Autumn is this particular variety, and I cut the top of it off and lift it off the fence in early winter, then cut it back to ~3'-4' off the ground each spring. Depending on the type of clematis you have, you may have different pruning requirements.

Here is a link that might be useful: {{gwi:587489}}

That's a lovely picture pianolady. This is a Gillian Blade and says it is a type 2 large flowered clematis. It can grow tall but won't be as bushy as a sweet autumn. My stockade fence is 6 ft. tall. A clematis might be able to wind around the boards in a picket fence but there is no opening between the boards in a stockade fence. I am still hoping to learn whether I can get it to grow up my fence with strings or something less visible than using wire netting or a trellis.

I'd try using wire instead of string, as the string might break or get chewed through by a critter. You could use small eye bolts to attach the wires to the fence. You could use several wires and create a fan effect, or place them horizontally depending on what effect you wanted.

That's a good idea, pianolady. Thanks.