In particle accelerator physics, superconducting magnets are crucial to achieve high-energy particle beams used in fundamental physics experiments. One of the key challenges of superconducting magnets is the transition of the superconducting material to the normal conducting resistive state—called quench—which could cause damage to the superconducting magnet volume, due to the large quantities of heat produced by ohmic losses in the material if the magnet is not properly protected. In this work, we train explainable machine learning models to detect the occurrence of quenches, starting from the harmonic decomposition of the magnetic field produced by the residual superconducting magnetization after a quench event and aiming at explaining the prediction process. A successful solution to this problem is a fundamental ingredient in the construction of a real-time predictive maintenance system. Indeed, interpretability paves the way to the construction of a tailored, efficient, and affordable system that only considers the relevant magnetic field harmonics. We show that quenches can be detected with high accuracy by rather simple models, and we also describe some preliminary but encouraging results on the quench localization problem.