In a thin and large area PZT-ceramics piezoresonator (PR) with relatively low resonance impedance, caused by high-frequency resonance and high PR capacitance, the effect of electrode resistivity and parasitic resistive and inductive elements in the measurement fixture results in significant distortion of the measured thickness-mode (longitudinal TL, shear TS) resonance response-resonance frequency shifts and characteristics deformation. This distortion may not allow the precise measurement of the PR characteristic frequencies, quality factor, and electromechanical coupling coefficient so essential to a complete PR and material characterization. A theoretical description of the "energy-trap" phenomena in a thickness-vibrating PR with resistive electrodes is presented. To interpret electrical measurements, the electromechanical model, including for completeness both the PR with resistive electrodes (as a system with distributed parameters) and the measurement fixture, is developed. The method of two contact points on the electrode provides deep sharpening and exact determination of the PR resonance. For the optimal disposition of the contact fingers, the resonance bandwidth of a real PR with resistive electrodes is even more pointed than that for the ideal PR.