Yes you can move them. It's best to prune them when you do. You have to prune a clematis anyway. Move them when they're not flowering - between Oct and March probably for a honeysuckle. For Clematis it depends on it's flowering season. I suppose the best time for spring flowering ones would be after they finish flowering. The summer and autumn flowering ones would be best moved in late winter or spring.
Plant the Clematis deeply in the ground.
Hope this will help you :o)