The friendly gardener with the clematis Montana 'Continuity' growing gets a six inch pot, fills it with compost, and buries it in the soil near the clematis. They split a stem and stick a bit of wood in between each half, then bury this in the compost within the pot. Eventually some roots will grow, and it can be cut off from the mother plant. Then you can meet them for a cup of tea, and pick up your very own 'Continuity'. In theory. I've never tried it myself.. I just read lots of books about propagation.
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This gives a good explanation: https://www.flowerpatchfarmhouse.com/propagate-clematis-layering/
http://www.clematis-nursery.co.uk/clematis-c.htm