Double-perovskite oxides Ca2MgOsO6 and Sr2MgOsO6 have been synthesized under high-pressure and high-temperature conditions (6 GPa and 1500 degrees C). Their crystal structures and magnetic properties were studied by a synchrotron X-ray diffraction experiment and by magnetic susceptibility, specific heat, isothermal magnetization, and electrical resistivity measurements. Ca2MgOsO6 and Sr2MgOsO6 crystallized in monoclinic (P2(1)/n) and tetragonal (I4/m) double-perovskite structures, respectively; the degree of order of the Os and Mg arrangement was 96% or higher. Although Ca2MgOsO6 and Sr2MgOsO6 are isoelectric, a magnetic-glass transition was observed for Ca2MgOsO6 at 19 K, while Sr2MgOsO6 showed an antiferromagnetic transition at 110 K. The antiferromagnetic-transition temperature is the highest in the family. A first-principles density functional approach revealed that Ca2MgOsO6 and Sr2MgOsO6 are likely to be antiferromagnetic Mott insulators in which the band gaps open, with Coulomb correlations of similar to 1.8-3.0 eV. These compounds offer a better opportunity for the clarification of the basis of 5d magnetic sublattices, with regard to the possible use of perovskite-related oxides in multifunctional devices. The double-perovskite oxides Ca2MgOsO6 and Sr2MgOsO6 are likely to be Mott insulators with a magnetic-glass (MG) transition at similar to 19 K and an antiferromagnetic (AFM) transition at similar to 110 K, respectively. This AFM transition temperature is the highest among double-perovskite oxides containing single magnetic sublattices. Thus, these compounds offer valuable opportunities for studying the magnetic nature of 5d perovskite-related oxides, with regard to their possible use in multifunctional devices.