A piezoelectric energy harvester (PEH) is composed of an electromechanical structure along with an electric circuit. The objective of such a device is converting otherwise unused mechanical energy into electrical energy to power e.g. wireless sensors. The piezoelectric effect, used as the energy conversion principle, describes the generation of electric voltage when the piezoelectric material is mechanically deformed and vice versa. The finite element method (FEM) allows for the simulation of arbitrarily shaped and nonlinear electromechanical structures, while an electronic circuit simulator (ECS) can be applied to simulate arbitrary electric circuits. A novel implicit FEM-ECS coupling method is proposed, which combines the advantages of the FEM and the flexibility of an ECS. The Newton-Raphson method is applied to achieve equilibrium at the interface between the FEM and ECS simulations, so that arbitrary PEHs can be efficiently analyzed. An application example consisting of a nonlinear electromechanical structure and a self-powered advanced electric circuit is considered and a shock-like base excitation is applied. This example demonstrates the practical applicability of the novel coupling method for realistic system simulations of PEHs.