Elliptical retarders have important applications in interferometry and polarimetry, as well as imaging and display technologies. In this work, we discuss the traditional elliptical retarder decomposition using Pauli matrices as basis sets and then introduce a solution to the inverse problem: how an arbitrary elliptical retarder with desired eigenpolarizations and retardance can be constructed using a combination of linear and circular retarders. We present a simple design process, based on eigen-decomposition, with a solution determined by the intrinsic properties of each individual retarder layer. Additionally, a novel use of cholesteric liquid crystal polymer as a circular retarder is presented. Through simulation and experimental validation, we show cholesteric phase liquid crystal has an achromatic region of circular retardance at shorter wavelengths, outside of the Bragg regime. Finally, we verify our design process by fabricating and testing an elliptical retarder using both nematic and cholesteric phase liquid crystal polymers. The performance of the elliptical retarders shows excellent agreement with theory.