The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We determine the variation of the oscillator frequency as a function of its orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike test) with respect to a preferred frame candidate. We constrain the corresponding parameters of the Mansouri and Sexl test theory to delta-beta + 1/2 = (1.5+/-4.2) x 10(-9) and beta-alpha - 1= (-3.1+/-6.9) x 10(-7) which is of the same order as the best previous result for the former and represents a 30-fold improvement for the latter.