Ba[(Mg1/3Nb2/3)(1-x)Hf-x]O-3 (BMNH, x = 0.05, 0.1, 0.15, 0.2) solid solutions were prepared via the solid-state reaction method. The effect of BaHfO3 on the crystal structure, microwave dielectric performance, and defect relaxation behavior of Ba(Mg1/3Nb2/3)O-3 (BMN) were studied. BaHfO3 additions degraded the sintering activity of BMN powder, requiring a high sintering temperature (T-s) similar to 1650 degrees C; but it could be effectively improved by a prolonged sintering process at a lower T-s of 1600 degrees C. The well-sintered BMNH ceramics (1600 degrees C for 30 h) possessed a high densification >96%, and exhibited cubic perovskite structures without 1:2 cation ordering. Once doped with Hf, the low-temperature relaxation in dielectric spectroscopy and thermally stimulated depolarization current (TSDC) for pure BMN disappeared, further indicating such relaxation is related to cation-ordered structure. Oxygen vacancies, namely showing in-grain and across-grain-boundary relaxation of Vo-related defects, were the main defect types in BMNH. The concentrations of in-grain Vo decreased as x increased, which is beneficial to BMNH to maintain high Q x f values of 69 400-73 000 GHz. Accompanied by a high epsilon(r) of 33.27-33.59 and a low (f) of +13.6 to +20.7 ppm/degrees C, these materials have a good potential for applications in microwave components and devices.