The structural and magnetic properties of unique single-ion manganese-based multiferroic perovskites Sr_1-xBa_xMn_1-yTi_yO₃ (SBMTO) were investigated by XRD. For compounds near x = 0.45–0.65 and y = 0–0.1, a cubic to non-centrosymmetric tetragonal transition takes place below ~ 430 K on heating and at ~ 60 K lower temperature on cooling. Ferroelectric (FE) distortions c/a that are larger than the P4mm distortions of nonmagnetic BaTiO₃ have been observed with maximum estimated polarization of ~ 29 μC/cm² at ~ 220 K. At lower temperatures, the polarization is suppressed by ~ 40 % due to development of antiferromagnetic (AFM) phase, indicating very strong coupling between FE and AFM. The FE phase is rapidly suppressed by hydrostatic pressure.