Lots of clematis flower prolifically enough to grow for cutting and those listed below are the best for a particularly good display while lasting well in water.
Also consider plants from these groups:
Atragene Group - Spring flowering with nodding bell-like flowers.
Diversifolia Group - All the clematis in this group are suitable to use as cut flowers.
Heracleifolia Group - Many of these stunning herbaceous plants are also scented.
Integrifolia Group - They are all suitable to use as cut flowers.
Tangutica Group - Not only extremely free flowering but they produce excellent seedheads for added interest in the winter months.
Texensis Group - Exotic looking plants, many with trumpet shaped flowers that are ideal for flower arranging.
Viticella Group - They are all extremely hardy, very free flowering, they cannot be recommended highly enough.