We describe the results of an experiment to test for spacetime anisotropy terms that might exist from Lorentz violations. The apparatus consists of a pair of cylindrical superconducting cavity-stabilized oscillators operating in the TM010 mode with one axis east-west and the other vertical. Spatial anisotropy is detected by monitoring the beat frequency at the sidereal rate and its first harmonic. We see no anisotropy to a part in 10(13). This puts a comparable bound on four linear combinations of parameters in the general standard model extension, and a weaker bound of < 4 x 10(-9) on three others.