Many researchers have investigated the possibility of amplifying ambient vibrations and converting the associated kinetic energy into usable electric energy. The vast majority of vibration harvesting devices use mechanical oscillators to boost the amplitude of vibration; however, this can result in a rather narrow band of excitation over which the harvesting device is effective. One approach proposed to overcome this limitation is to substitute the conventional linear oscillator with an oscillator featuring a non-linear compliance characteristic: these mechanisms produce broader frequency responses. The design and optimization of nonlinear energy harvesting devices is however not trivial and there is no consensus among the publish works that the benefits of non-linear oscillators can be realized in the energy harvesting context. This work attempts to further develop understanding of nonlinear energy harvesters by investigating the optimum resistive load. The definition of an optimal load for the nonlinear device is first considered, given due consideration to bandwidth and stability of the operating point, and comparisons with linear devices is shown. Finally, the issue of multiple solutions in the frequency response is addressed.