Some good and creative guesses about why the Clematis leaves had interveinal necrosis. While iron and manganese deficiencies both cause interveinal chlorosis (veins are green, areas between are yellow), the necrosis indicates tissue death between the still-living and green veins. Very simply, this has been caused by water loss.
During transplanting of the vine, I had to remove them from the fence and lay them out on the ground. They remained this way for a couple of days. For much of the foliage, this meant that the lower leaf surfaces were now exposed to the sun. As with many broadleaved plants, the upper and lower leaf surfaces are morphologically distinct: the upper surfaces have a thicker waxy cuticle and epidermis, with few stomata, while the lower surface lacks much of the cuticle and is loaded with stomata. When the leaves are turned upside down, the shade-adapted lower surfaces now receive intense sun exposure: water evaporates quickly from these unprotected leaves and the tissue dies. The only parts of the leaf that don’t die are the veins, which remain full of water as long as the roots are functional.
So both LisaB and Benjamin identified sun exposure as the culprit behind the damage. But as with many environmentally-induced plant problems, the ultimate cause is water stress.