Extracting energy from motion and vibration is an attractive route to powering wireless sensors, and MEMS (micro-electro-mechanical-systems) technology is well suited to miniaturizing such generators. Most reported MEMS motion-driven scavengers use linear displacement, and have very restricted output power. Here two alternatives are proposed and analyzed: resonant rotating generators, in which the angular amplitude of the proof mass is greater than that of the source motion, and gyroscopic scavengers, in which the proof mass is actively spun or vibrated. By avoiding, respectively, the linear displacement limit and the limited mass of conventional devices, it is shown that large increases in obtainable power are possible, particularly if parasitic damping is minimized.