The Kurt Vonnegut Speculative Fiction Prize is run by the North American Review, the oldest literary magazine in the United States (having been founded way back in 1815). The competition is seeking speculative fiction of all kinds. Though it doesn’t have to be directly influenced by Vonnegut’s work, it can be (and it surely couldn’t hurt your chances!).
With a tidy first prize of $1,000 and possible publication in North American Review, this is a competition worth entering for anyone interested in writing speculative fiction.