We consider nontrivial finite energy traveling waves for the Landau--Lifshitz equation with easy-plane anisotropy. Our main result is the existence of a minimal energy for these traveling waves, in dimensions two, three, and four. The proof relies on a priori estimates related to the theory of harmonic maps and the connection of the Landau--Lifshitz equation with the kernels appearing in the Gross--Pitaevskii equation.