In this paper, we present a nonlinear electromagnetic energy harvesting device that has a broadly resonant response. The nonlinearity is generated by a particular arrangement of magnets in conjunction with an iron-cored stator. We show the resonant response of the system to both pure-tone excitation and narrow-band random excitation. In addition to the primary resonance, the superharmonic resonances of the harvester are also investigated and we show that the corresponding mechanical upconversion of the excitation frequency may be useful for energy harvesting. The harvester is modeled using a Duffing-type equation and the results are compared with the experimental data.