The rovibronic (rotation–vibration–electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the A˜2Π–X˜2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X˜2Σ+ and A˜2Π electronic states along with A˜–X˜ transition dipole moment surfaces (DMSs). For the ground X˜2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm−1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the A˜2Π state PESs and A˜–X˜ DMSs. Variational calculations consider both Renner–Teller and spin–orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the A˜2Π state, line list calculations up to J = 125.5, and an analysis of Renner–Teller splittings in the ν2 bending mode of CaOH are discussed.