Yes you should be able to do this with any type of honeysuckle. It is fairly easy. It is best if possible to do this in the spring when the first new growth appears but you can do it indoors most any time of year.
Cut a length of the green soft portion of the vine and make to get a good number of sets of leaves. Trim the leaves off of the cut end. You should end up with one or two leaf nodes bare and one or two sets of leaves left on the opposite end of the cutting.
There are two good ways to get the new plant to produce a root system. The first option is to dip the honeysuckle cutting in rooting hormone and plant it in damp rooting or potting soil. These can both be purchased online or from a local gardening store or nursery.
The other option is to place the cutting in a vase or cup of water. If you choose this method, be sure to change the water fairly often to prevent the new plant from rotting.
With either method, you should see roots begin to form. When you have several good roots of at least an inch long you can permanently plant the new honeysuckle plant.
