The determination of complex elastic, piezoelectric, and dielectric coefficients of piezoelectric ceramics is important for precision engineering devices. Here, a novel method for determining the optimal material coefficients is presented. This method minimizes the average relative error in the values of conductance, susceptance, resistance, and reactance obtained from the 1-D model in the IEEE Standard (ANSI/IEEE Std 176-1987) and the experimental measurements of the first and second radial modes. Poisson's ratio is assumed to be a complex number in addition to the elastic, piezoelectric, and dielectric coefficients in the present method. The global minimum of the average relative error is found by searching the minimum among all local minima of the average relative error, which are obtained with the Levenberg-Marquardt modification of Newton's method from randomly chosen initial conditions. The optimal material coefficients of an APC 850 disk and an APC 855 disk are calculated with this method. The uncertainties in the optimal material coefficients are evaluated by calculating the minimum average relative error when the real or imaginary part of each coefficient is prescribed.