Searches for time-reversal symmetry (T) violations using spin sensors are susceptible to spurious frequency shifts and noise from magnetic fields, which can mask signals originating from beyond-standard-model new physics. Therefore, a comagnetometer—an auxiliary sensor that allows mundane magnetic-field effects to be differentiated from new physics—is an essential feature of many precision measurements. We characterize an intrinsic comagnetometer that is available in crystals, which can be used to suppress spurious magnetic-field effects through comparing sets of ions related by spatial reflection symmetry. We find that the new-physics measurement channel can be effectively shielded to better than 10 µG, without the need for active or passive magnetic shields. Our measurements demonstrate precise and accurate control over magnetic systematic errors, laying the groundwork for improved searches of T violation using solid-state systems.