We present a mathematical Inverse Method providing reliable material parameters of piezoceramic materials. Thereby, a systematic matching of finite element simulations to measurements yields the complete set of material parameters. Contrary to our previous research where we utilized both, frequency resolved electrical impedances and spatially resolved surface velocities, only the impedance curves serve as input quantity of the enhanced Inverse Method. Within this method, two block shaped piezoceramics of equal geometric dimensions but different directions of electrical polarization are investigated. For the piezoceramic material PIC255, the identified material parameters exhibit to some extent deviations from the manufacturer's parameters of more than 20 %. For verification purposes, we perform finite element simulations of a discoidal piezoceramic material which was not considered for the Inverse Method. Comparisons with measurements demonstrate that the identified parameters can be used to precisely predict the behavior of piezoceramic materials.