The Sr(Ga0.5Ta0.5)O3-based perovskites with O2- and/or Sr2+ vacancies were formed by changing the A-site and/or B-site cation ratios. The Sr-deficient perovskites with a limited composition of Sr0.86(Ga0.36Ta0.64)O3 could be obtained, whereas oxygen vacancies were hardly created. The B′-site Ga3+ cation could be replaced with large Sc3+, In3+, Y3+, Nd3+ and La3+. The crystal symmetry of the complex perovskites changed from cubic (B′=Ga3+, Sc3+, In3+) to tetragonal (B′=La3+) through rhombohedral (B′=Y3+, Nd3+). The dielectric permittivities of these ceramics indicated no distinct dependence on the B′-site cation species. The temperature coefficient of permittivity might be associated with the symmetry change of the perovskite phases. Higher microwave Qf values, >Qf=38 000 GHz, were obtained for our complex perovskite ceramics, except with B′=La3+.