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 \(\tilde{A}\,^2\Pi\)--\(\tilde{X}\,^2\Sigma^+\) band system of CaOH using high-level \textit{ab initio} theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the \(\tilde{X}\,^2\Sigma^+\) and \(\tilde{A}\,^2\Pi\) electronic states along with \(\tilde{A}\)--\(\tilde{X}\) transition dipole moment surfaces (DMSs). For the ground \(\tilde{X}\,^2\Sigma^+\) state, a published high-level \textit{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 (rms) error of 0.06~cm\(^{-1}\). Large-scale multireference configuration interaction (MRCI) calculations using quintuple-zeta quality basis sets are employed to generate the \(\tilde{A}\,^2\Pi\) state PESs and \(\tilde{A}\)--\(\tilde{X}\) 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 \(\tilde{A}\,^2\Pi\) state, line list calculations up to \(J=125.5\), and an analysis of Renner-Teller splittings in the \(\nu_2\) bending mode of CaOH are discussed.