Miniature and energy-efficient propulsion systems hold the key to maturing the technology of swimming microrobots. In this paper, two new methods of propulsion inspired by the motility mechanism of prokaryotic and eukaryotic microorganisms are proposed. Hydrodynamic models for each of the two methods are developed, and the optimized design parameters for each of the two propulsion modes are demonstrated. To validate the theoretical result for the prokaryotic flagellar motion, a scaled-up prototype of the robot is fabricated and tested in silicone oil, using the Buckingham PI theorem for scaling. The proposed propulsion methods are appropriate for the swimming robots that are intended to swim in low-velocity fluids.