We report a new approach for designing high-performance microelectromechanical system (MEMS) electromagnetic energy harvesting devices, which can operate at low frequency (<;1 kHz) over the ultrawide bandwidth of 60-80 Hz. The output power from the devices is increased significantly at a low optimized load and this overall enhancement in performances is benchmarked using a "power integral (Pf)" figure-of-merit. The experimental results show that the efficient nonlinear designs produce large Pf values, giving rise to one of the highest normalized Pf densities among the reported MEMS scale nonlinear energy harvesting devices. This improvement is achieved by suitably designing the nonlinear spring architectures, where the nonlinearity arises from the stretching strain of the specifically designed fixed-fixed configured spring arms under large deflections and gives rise to wideband output response. Different fundamental modes of the mechanical structures are brought relatively close, which further widens the power-frequency response by topologically varying the spring architectures and by realizing the same using the thin silicon-on-insulator substrate using MEMS processing technology. In addition, we have used the magnet as proof mass to increase the output power in contrary to conventional approach of using the coil as the proof mass in micro-electromagnetic energy harvesters. The high performance obtained from the MEMS energy harvesters with integrated double layer micro-coil is compared with the same using wire wound copper coil. The experimentally obtained results are qualitatively explained by using a finite-element analysis of the designed structures.