I have used many different vines to grow on the wire fences and trellises at Dawn Gardens. Here are a few of them:
Chilean Bellflower (Lapageria rosea). National flower of Chile.
Very slow growing. Also available in pink. Part shade.
Variegated Porcelain Berry (Ampelopsis brevipedunculata ‘Elegans’) The birds and the bees love these berries which are green, purple, rose, blue, white and pink. Deciduous Vine.
California Dutchman’s Pipe (Aristolochia californica) Deciduous vine native to California.

Holboellia coriacea

Kangaroo Treebine (Cissus antarctica). Killed when the temperature got down to 30 degrees.
Evergreen Clematis (Clematis armandii) – very fragrant
Anemone Clematis (Clematis montana)

Clematis ‘Avalanche’
Sweet Autumn Clematis (Clematis terniflora) blooms late summer to fall.

Clematis ‘Nellie Moser’
Clematis ‘Multi Blue’
Clematis ‘Rouge Cardinal’

Clematis ‘Jackmanii’
Clematis ‘Jackmanii Superba’
Lilac Vine (Hardenbergia violacea) Evergreen vine from Australia. Killed when the temperature got down to 29 degrees.
Carolina Jessamine (Gelsemium sempervirens) Deer resistant
Silvervein Creeper (Parthenocissus henryana) has pink to red fall color.