Fill a 6-inch diameter pot with a sterile potting mix. Make your own by combining equal parts peat moss and vermiculite. Water the mix until it's moist throughout so mix is ready to receive the cutting.
Cut off a shoot from new wood that has four to six healthy buds and leaves. Make the cut 1/8 inch above a bud on the shoot, using a sharp, clean knife.
Dip cut surface of the clematis shoot in a rooting hormone, available from garden centers. The hormone encourages quick root production and helps prevent disease from invading the shoot through its cut surface.
Push the bottom third of the cutting into the potting mix so it stands upright. Cover the pot with a clear plastic bag.
Keep the pot in a warm area that receives bright, indirect light. Water the potting mix if it begins to dry out, as the cutting must remain moist at all times.
Remove the bag once the cutting roots, usually within four to eight weeks. Rooted cuttings usually have new growth on their shoot or the buds begin to swell. Keep the cutting watered and provide warmth and light until you are ready to transplant it outdoors in spring.