Piezoelectric shunt damping is a well known technique to damp the mechanical vibrations of structures. Due to the piezoelectric effect, the piezoceramics converts mechanical energy into electrical energy. Connecting electrical networks to the electrodes of the piezoceramics allows to dissipate a part of this energy in the electrical shunt. Linear resonant shunts consisting of inductance and resistance (LR) are broadly used, but their damping performance is limited. Adding a negative capacitance to the LR-shunt can significantly increase the performance, but these networks are prone for instability. This paper determines the damping performance of negative capacitance shunts. The optimal tuning of the network parameters are presented as well as the maximum energy dissiption and the stability margin. The results are validated by measurements.