A Complementary Metal Oxide Semiconductor (CMOS) power switching circuit and a method for operating a CMOS power switching circuit are described. In one embodiment, a CMOS power switching circuit includes a voltage selection circuit configured to output the highest output voltage between an output voltage of a primary power supply and an output voltage of a backup power supply and a control circuit configured to connect a load circuit to either the primary power supply or the backup power supply by comparing the output voltage of the primary power supply with a power supply switchover level that is set as a function of the highest output voltage. The backup power supply serves as a voltage reference to set the power supply switchover level only when the output voltage of the primary power supply is lower than the output voltage of the backup power supply. Other embodiments are also described.