A retarder is presented for application in systems that transmit radiation through waveguides, such as microwave or millimeter-wave systems. The retarder is a compound device comprising multiple single element retarders, each of which introduces a retardation phase between different polarization states, and each of which is set at an orientation angle. The phases and angles are selected to maximize the operational bandwidth of the compound retarder. The selection of the phases and angles may be found by solving a set of simultaneous equations.