Run eye screws up the post, set about 8 -12 inches apart, then string 14 or 16 gauge wire through the eyes. Wind the wire around the end eyes or use a wire tightener to keep the wire tight.

The other thing you could do is spray paint the wire to match the background of what the wire is in front of. Use a colored Rustoleum flat or satin. I use a tan color , against my treated wood deck railings. I think it looks less noticeable.

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Try high test fishing line rather than the wire. One, it is virtualy invisible and two, it won't heat up in the sun like wire can and damage tender new growth.

I was going to post the 18 gauge wire. Trust me, you will not see it! I know that by experience. Sounds nice, your cedar structure.

gardengal always has such great ideas. fyi to others but not for you: on our driveway, we have an antique dark green painted pergola/entrance into our gardens We grow potted clematis up its posts, first wrapping black plastic melon netting around the posts and securing it w/ dark green twist-ties.
best,
mindy