In this paper, a new tuning method for shunt damping with a series resistance, inductance and negative capacitance is proposed and its validity is investigated. It is based on the measured electromechanical impedance of a piezoelectric system, which is represented through an equivalent electrical circuit that takes into account the characteristics of the piezoelectric transducer and the host structure. Afterwards, an additional circuit representing the shunt is connected and the Norton equivalent impedance is obtained at the terminals that represent the mechanical mode of interest. During the tuning process, the optimal shunt parameters are found by minimizing the maximum absolute value of the Norton equivalent impedance over a defined frequency range through a numerical optimization. Taking benefit from the analogy between electrical impedance and mechanical admittance, the minimization of different mechanical responses (displacement, velocity or acceleration) is also proposed and the different optimum shunt parameters obtained are compared. In view of real technical applications, this method allows the integration of a real negative capacitance circuit, i.e., a negative impedance converter, rather than an ideal component. It is thus possible to use the impedance of this circuit and optimize the individual component values. Since this method is based on one simple measurement, it can be applied to arbitrary structures without the need of complex dynamic tests or expensive finite elements calculations. Finally, an experimental analysis is carried out in order to compare the damping performance of the proposed method and the conventional analytical method that minimizes a mechanical frequency response function.