This article addresses piezoelectric shunt damping through a resonant shunt associated with negative capacitances. The main objective of this article is to provide guidelines for choosing the best electrical circuit layout in terms of control performance and possible stability issues. This article proposes general analytical formulations for the tuning/optimisation of the electrical shunt impedance and for the prediction of the attenuation performance. These formulations are demonstrated to be valid for all the possible configurations of the negative capacitances. It is demonstrated that the behaviour of the different shunt circuits can indeed be described by a common mathematical treatment. Moreover, the use of two negative capacitances together is shown to provide benefits compared to traditional layouts based on a single negative capacitance. The mentioned advantages relate to both stability and attenuation performance. The use of a resonant shunt with the addition of negative capacitances is finally proven to provide enough attenuation to even cancel eigen frequency peaks in some cases. This article also analyses the main issues arising from the practical implementation of the negative capacitances. Finally, the theoretical results are validated through experiments conducted on a cantilever beam coupled to two piezoelectric patches.