The high-frequency nature of impedance-based structural health monitoring makes the utilization of impedance signature for model-based damage characterization a challenging problem. In this study, a novel damage characterization approach that utilizes impedance signature measured with a single piezoelectric wafer is developed. Length-varying spectral elements are introduced to minimize the total number of elements required to describe the system, along with the number of damage characterization parameters. Several objective function definitions are studied and their behaviour with respect to each damage parameter is investigated. It has been found that an objective function definition based on the frequency shift in impedance peaks is the most effective definition compared to root mean square deviation and correlation-based objective functions. A novel damage localization method, referred to as sine-fit localization method, is developed based on the underlying periodic behaviour of impedance peak shifts as a function of damage location. The sine-fit localization method is integrated with gradient descend method in a two-stage optimization algorithm for damage characterization. The developed algorithm is capable of solving the ill-posed problem of damage characterization with few iterations and small number of objective function evaluations, which makes it computationally very efficient.