There are those folks out there that use honeysuckle almost exclusively for their weaver. The Cherokee's still use a lot of native and Japanese honeysuckle in their work in random weave, twining, twill and rib basketry. Most of what I've used it for over the years tends to be as an additional sculptural element. The reason why is that the make up of the vine lends itself to being celebrated as a special feature, not just a normal weaver.
"Identification: Japanese Honeysuckle is an evergreen woody vine that may reach 80 feet in length. The leaves are opposite and elliptically shaped. The tan vine may reach a thickness of 2 inches in diameter. Fragrant, white or pale yellow tubular flowers appear in April to August. Spherical, black glossy berries containing 2 to 3 seeds mature from June to March.
Ecology: Japanese Honeysuckle is a common invasive plant in the Southeast. The shade tolerant vine occurs along field edges, right-of-ways, under dense canopies, and high in canopies. This invasive vine colonizes by prolific vine growth and seeds that are spread by birds" from http://www.ncsu.edu
Once you get your vines, you can store them in a cool, dry place until you're ready to use them. Just like the image here from one of my recent basket weaving classes, I recommend that you coil the vines into loose coils. However, be sure that they are small enough to fit in whatever pot you're going to use to boil them when you're ready to weave. Which brings me to the next step.
Now that you have your honeysuckle all boiled and cleaned you'll probably be ready for a nap! Welcome to weaving with natural materials :) However, now the fun begins. I usually separate my prepared materials by size. Large, gnarly pieces are great for handles, long straight pieces for weaving and then medium crooked pieces for weaving or as an architectural element on other baskets. Whatever it is, you'll want to weave while the vines are wet and pliable.
Hope this article helps you feel confident in going out and harvesting your own honeysuckle vines!