Answer: Your trellises sound lovely. For a sunny spot you might try some of the smaller annual vines such as morning glories, nasturtiums, or perhaps cardinal climber which has a fine texture. For part shade, asarina is lovely.
Since the trellises are rather small, in my experience the best perennial vines to consider would include the smaller clematis vines which will do well in sun or part shade and come in a wide variety of colors.
Good luck with your project!
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