When high quality bismuth or graphite crystals are placed in a magnetic field directed along the c axis (trigonal axis for bismuth) and the temperature is lowered, the resistance increases as it does in an insulator but then saturates. We show that the combination of unusual features specific to semimetals, i.e., low carrier density, small effective mass, high purity, and an equal number of electrons and holes (compensation), gives rise to a unique ordering and spacing of three characteristic energy scales, which not only is specific to semimetals but which concomitantly provides a wide window for the observation of apparent field-induced metal-insulator behavior. Using magnetotransport and Hall measurements, the details of this unusual behavior are captured with a conventional multiband model, thus confirming the occupation by semimetals of a unique niche between conventional metals and semiconductors.