Rachel, The stems of clematis turn woody as they mature. Cut away the the dead part that has browned. If the plant had wilt all the leaves would die, so I think your fine. Keep it watered so the soil stays moist, not sodden. Not all clematis are good for containers, dwarf or slow growing varieties are best. Look for varieties including "Bees Jubilee," "Carnaby," "Dawn," "Fireworks," "Lady Northcliffe," and "Royalty." Choose a large pot 16 to18 inches and plant the root ball 2-inches below the soil line. Fertilize monthly with a 10-20-10 fertilizer. Best And Happy Yardening, Nancy.