We experimentally investigate the usefulness of softening springs in a microelectromechanical systems electrostatic energy harvester under colored noise vibrations. It is shown that the nonlinear harvester has performance benefits when the vibration's center frequency varies in the frequency range of its softening response. With a vibration 3-dB bandwidth of 50 Hz, less than 3-dB variation in output power can be obtained over a 85-Hz wide range of vibration center frequencies. Compared to a simulated linear-spring device, the nonlinear device gives more output power for a wide range of vibration bandwidths. The nonlinear device shows less than 1-dB variation in output power when the vibration bandwidth varies from 12 to 120 Hz and is centered on the resonant frequency.