I've not done cuttings but many years ago [40+] my dad snapped some wild honeysuckle off a hedgerow and plunged the semi woody stem into a deep pot of garden soil. he kept it well watererd and it rooted.
I think you would need semi ripe wood to be successful. failing that layer it. Peg a semi ripe stem down into the soil and as long a sectional node[where leaves come off the stem] is buried it should root.

A climbing honeysuckle?
In Spring taking 6-8 inch cuttings from growing tips should work. Snip off all but the top leaves, put up to 8 cuttings into a 4 inch pot of fresh, new compost & cover with a clear plastic bag. Place in moderate light.

I had most success by bending the stems to the ground and layering them. (See Youtube for method).

here is the link to the RHS page and it describes several methods.
https://www.rhs.org.uk/plants/popular/honeysuckle/climbing/growing-guide

Thanks every one for your advice.
Eileen I have looked on the RHS site, it is very helpful,thank you.