Effects of postdensification annealing upon microstructures and microwave dielectric characteristics in Ba((Co0.6-x/2Zn0.4-x/2Mgx)(1/3)Nb-2/3)O-3 (x=0, 0.1, 0.2, and 0.3) complex perovskite ceramics have been investigated. Long-time annealing at temperatures below the order-disorder transition temperature enhances the cation ordering degree and promotes the ordering domain growth. The most significant improvement of Qf value is obtained together with the suppressed temperature coefficient of resonant frequency in the samples annealed at 1400 degrees C for 12h, while the dielectric constant decreases slightly. The Qf value of ceramics annealed at 1400 degrees C mainly attributes to the enhanced cation ordering degree, because their low-energy domain boundaries are not detrimental to the Qf value. As the annealing temperature increases close to the transition temperature, coarse ordering domains with high-energy boundaries are formed, and then the Qf value steadily decreases because of the inferior domain structure, even the cation ordering degree increases. The microwave dielectric characteristics of Ba((Co0.6-x/2Zn0.4-x/2Mgx)(1/3)Nb-2/3)O-3 ceramics are affected by the common function of ordering degree and domain structure. The best combination of microwave dielectric characteristics is obtained in the composition of x=0.3 after annealing at 1400 degrees C for 12h: epsilon(r)=33.2, Qf=117200GHz, and (f)=8.6ppm/degrees C.