An investigation of Ca substitution in the multiferroic material BiFeO3 shows that a wide range of perovskites BixCa1-xFeO3 (0.4 <= x <= 1.0) can be prepared by sintering in air at 810-960 degrees C. 0.4 <= x < 0.8 samples are cubic Pm<(3)over bar>m, whereas x = 0.8 and 0.9 show a coexistence of the cubic and the rhombohedral R3c BiFeO3-type structure. Considerable disorder arising from Bi3+ lone-pair distortions is evidenced by synchrotron X-ray and neutron studies of the average structures of the cubic phases, and electron microscopy reveals commensurate and incommensurate local superstructures. The BixCa1-xFeO3 (0.4 <= x <= 1.0) materials show a remarkably robust antiferromagnetic order with T-N = 623-643 K and ordered moments of 3.6-4.1 mu(B). They are "leaky" dielectrics with relative permittivities of similar to 30-100 and bulk resistivities similar to 50-500 k Omega cm at room temperature. The activation energy for bulk conduction increases from 0.27 eV for x = 0.4 to 0.5 eV for x = 1, but with a discontinuity at the cubic-rhombohedral boundary. Further processing of the x = 0.8 and 0.9 compositions to reduce conductivity through control of oxygen content could lead to improved BiFeO3-based multiferroics.