Dielectric properties and their related microstructural characteristics in solid solutions of (1 - x)Ba(Mg1/3Nb2/3)O-3-xSr(Mg1/3Nb2/3)O-3 (BMN-SMN, or BSMN) were investigated by measuring the relative permittivity (epsilon (r)), Q values, and temperature coefficient of resonator frequency (tau (f)), and by observing microstructure using transmission electron microscopy. When the tolerance factor (t) was > 0.99 in BSMN with composition 0 < x < 0.5, where the tilting of oxygen octahedra was not involved, the microstructure included only 1:2 ordered phase. In the region where 0.99 > t > 0.97 with 0.7 < x < 1.0, the phase due to the antiphase tilting of oxygen octahedral, the disordered phase, and the 1:2 ordered phase were also present. In a few of the grains, core-shell-type structures, whose main components were dislocations and stacking faults, were found in the solid solution of BSMN.