Violations of CPT symmetry and Lorentz invariance are searched for by studying interference effects in B-0 mixing and in B-s(0) mixing. Samples of B-0 -> J/psi K-S(0) and B-0(s) -> J/psi K+K- decays are recorded by the LHCb detector in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb(-1). No periodic variations of the particle-antiparticle mass differences are found, consistent with Lorentz invariance and CPT symmetry. Results are expressed in terms of the standard model extension parameter Delta a(mu) with precisions of O(10(-15)) and O(10(-14)) GeV for the B-0 and B-s(0) systems, respectively. With no assumption on Lorentz (non) invariance, the CPT-violating parameter z in the B-s(0) system is measured for the first time and found to be Re(z) = -0.022 +/- 0.033 +/- 0.005 and Im(z) = 0.004 +/- 0.011 +/- 0.002, where the first uncertainties are statistical and the second systematic.