Honeysuckle cuttings can be notoriously difficult to take, or so 'the books' would have us believe. I've been taking honeysuckle cuttings for years with 100% success.
The glorious perfume from these beautiful climbers make it well worth the effort to propagate them for free.
We are often told that if we want one cutting to root, then take 10/12. If I want one cutting to root, I 'take' one. You could be told to keep them in a propagator at a certain temperature, keeping them misted all through the winter, or put a plastic bag over them in a pot, don't let them get too wet, don't let them dry out, put some rooting powder in a glass of water and stand them in it until they root, etc. etc., - it's too much bother, and then you probably won't have any success. This is the way that works.
You can do this anytime the plants are not flowering, but after Autumn and just before Winter is best. If you are propagating from a plant in your garden, choose a long stem with plenty of shoots on it, lay it across the soil (don't detach it from the parent plant) and peg it down where there is growth shooting off it. If you haven't any pegs, a piece of wire curled into a 'U' shape will do, as will a rock or large stone. Don't go to any unnecessary expense. If you've ever potted up strawberry runners, you can do this.
This can be done in pots too, but during the bad winter weather, the pots can be knocked over and the 'rooting' cutting will be pulled out of the pot.
When you've done this, leave it, leave it, and leave it some more, then in the Springtime (about now) when you check you will see that you have loads of tiny rooted plants. I wouldn't detach them straight away, give them chance to put down deeper roots before moving them, or potting them up.
And there you have it - Honeysuckle plants for free without the hassle.