Measurements of CP observables in B-+/- -> DK*(+/-) decays are presented, where D denotes a superposition of D-0 and (D) over bar (0) meson states. Decays of the D meson to K-pi(+), K-K+, pi(-)pi(+), K-pi(+)pi(-)pi(+) and pi(-)pi(+)pi(-)pi(+) are used and the K*(+/-) meson is reconstructed in the K-S(0)pi(+/-) final state. This analysis uses a data sample of pp collisions collected with the LHCb experiment, corresponding to integrated luminosities of 1 fb(-1), 2 fb(-1) and 1.8 fb(-1) at centre-of-mass energies root s = 7TeV, 8TeV and 13TeV, respectively. The sensitivity of the results to the CKM angle gamma is discussed.