The products and microwave dielectric properties of ceramics were investigated which had nominal composition (Ba1-xCax)(B1/2B'(1/2))O-3 (B3+ = Y3+, Nd3+, Gd3+; B'(5+) = Nb5+, Ta5+). The products versus x relationships of these systems were complex, owing to the small amounts of the third and fourth compounds in a wide range of intermediate x. Dielectric properties of (Ba1-xCax)(Nd1/2Nb1/2)O-3, (Ba1-xCax)(Y1/2Nb1/2)O-3 and (Ba1-xCax)(Y1/2Ta1/2)O-3 systems were evaluated. Relative permittivities (epsilon(r)) of the first system changed linearly with x; however, those of the last two systems increased sharply to have respective peaks at x of 0.2, and then decreased with x. Those sharp increases in epsilon(r) were similar to those reported for (Ba1-xCax)(Mg1/3Ta2/3)O-3 and other systems. However, the relative values of the increase in epsilon(r) were different. Plausible mechanisms to explain those differences among systems are discussed by introducing an index of rattling of the Ca2+ ion. (C) 2002 Elsevier Science B.V. All rights reserved.