I am no expert on clematis.
But you could hold some paper over the soil, to hold it in place, and then carefully tip the pots onto their sides, to let all the water drain away.
I do have some large glazed pots. Most of mine do have holes, even if they are very small; though perhaps yours do not. Conceivably, someone who was expert, could dill a hole into the bottom of a pot, tipped on its side. In that case you could leave the plants in the pots, as they are.
Hopefully you'll get some much better answers, very shortly....