Microrobotic swarms actuated by magnetic fields have attracted considerable attention in the field of automatic control. Developing effective control schemes for microrobotic swarms to track multiple mobile targets is still a major challenge. In this work, we propose an optimized rapidly-exploring random tree star (ORRT*) algorithm to generate desired paths connecting the swarm and the targets. A path selection strategy is developed to select the shortest path, and subsequently the immediate target to track is determined. The sliding mode (SM) motion controller is then presented to achieve the tracking of multiple mobile targets using microrobotic swarms. Comparisons are performed to validate the effectiveness of the control scheme, including the path planner and the motion controller. Finally, simulations and experiments of tracking multiple mobile targets in a virtual micromaze are conducted.