Leave the plant leaves untouched immediately after the late-season frost as the damaged leaves can protect the plant if another late frost occurs. Wait until all danger of frost has passed before treating the clematis. Even a clematis that looks completely dead can regrow.
Water the soil around the clematis and keep the ground mulched with bark chip mulch to insulate the plant roots in the event of another frost.
Disinfect a pair of hand pruners in rubbing alcohol to prevent spreading disease to the clematis. If you previously cut a diseased plant with the pruners and don't disinfecting the blade, you can transfer the disease to the clematis and further decrease its chance of survival.
Cut away any black, brown, wilted or otherwise damaged plant material to completely remove the frost-damaged parts of the clematis. Cut back to just above a healthy, undamaged lateral branch, bud or leaf set. New growth is tender, so this might require cutting the entire plant back to the ground if you're dealing with a plant that died back to the ground in winter and sprouted from dormant roots. In most cases, you'll only have to prune the new growth tips of mature vines that go dormant without dying back to the ground.
Add a general-purpose fertilizer to the mulch around the plant and water it in to encourage new growth.