Clematis make an ideal cut flower. The delicate look of the flowers is a contradiction to their suitability for cuts. Clematis stems are fibrous and not easily damaged. In addition, this allows them to rehydrate easily. Most cut clematis will open bloom from buds indoors, and flowers will stay fresh for up to 10 days or longer.
When growing clematis with an eye to being able to cut the flowers, it is good to keep this in mind as you train your stems in early spring. While naturalized, scrambling stems can be used for cuts in lower arrangements, a straighter stem is sometimes easier to work with.
Train the stems you are planning to use for cuts on thin, 5 or 6 ft. bamboo canes. These are available at garden centers. Clip the stems to the canes, tie the stem with something soft and secure like a strip of fabric, or horticultural velcro that can be cut to size works well. By keeping the stems separate and not tangled, it will be easier to harvest longer stems for cut flowers.
Both flowers and flower buds can be cut. Place them in water, and use a product to extend the life of cut flowers in the water of your arrangement.