The microwave dielectric characteristics of (1-x)(Al$\_$$frac{1}{2}$/Ta$\_$$frac{1}{2}$/)O$_2$-x(Mg$\_$1/3/Ta$\_$2/3/)O$_2$ (0$leq$x$leq$1.0) ceramics were investigated by crystalstructure, variations of ionic polarizability, and microstructures. As x increased, (1-x)(Al$\_$$frac{1}{2}$/Ta$\_$$frac{1}{2}$/)O$_2$-x(Mg$\_$1/3/Ta$\_$2/3/)O$_2$ transformed to tetragonal structure. Because the ionic radius of (Mg$\_$1/3/Ta$\_$2/3/)$^$4+/was slightly bigger than one of (Al$\_$$frac{1}{2}$/Ta$\_$$frac{1}{2}$/)$^$4+/, the cell parameters increased with increase of (Mg$\_$1/3/Ta$\_$2/3/)O$_2$concentration and coincided with prediction of the molecular additivity rule. As x increased, the compositions revealed ordered phase and were of single phase above 60 mol%. The increase of the ordered phase and grain size enhanced the Q and when ordering was completed at x over 0.6, the grain size was major factor for the increase in the a. Though the grain size increased, however, the porosity deteriorated the q. Therefore, the a depended on the order/disorder, the porosity, and the grain size in regular order.