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Ceramics in the solid solution system, (1 − x)Ba0.8Ca0.2TiO3xBi(Mg0.5Ti0.5)O3, were prepared by a conventional mixed oxide route. Single-phase perovskite-type X-ray diffraction patterns were observed for compositions x < 0.6. A change from tetragonal to single-phase cubic X-ray patterns occurred at x ≥ 0.1. Dielectric measurements indicated relaxor behavior for x ≥ 0.1. Increasing the Bi(Mg0.5Ti0.5)O3 content improved the temperature sensitivity of relative permittivity ϵr at high temperatures. At x = 0.5, a near-plateau relative permittivity, 835 ± 40, extended across the temperature range, 65°C–550°C; the permittivity increased at x = 0.6 to 2170 ± 100 for temperatures 160°C–400°C (1 kHz). The corresponding loss tangent, tanδ, was ≤0.025 for temperatures between 100°C and 430°C for composition x = 0.5; at x = 0.6, losses increased sharply at >300°C. Comparisons of dielectric properties with other materials proposed for high-temperature capacitor applications suggest that (1 − x)Ba0.8Ca0.2TiO3xBi(Mg0.5Ti0.5)O3 ceramics are a promising base material for further development.