We introduce the theory and a proof-of-concept design for MEMS-based, diamagnetically-levitated accelerometers. The theory includes an equation for determining the diamagnetic force above a checkerboard configuration of magnets. We demonstrate both electronic probing and a rapid MEMS-based interferometer technique for position sensing of the proof mass. Through a proof-of-concept design, we show electrostatic-measurement sensitivity achieving 34 mug at a 0.1 V sense signal and interferometer-measurement sensitivity achieving 6 mug for in-plane vibrations at 5 Hz. We conclude by outlining batch-fabrication steps to produce levitated accelerometers.