The ability to design quantum systems that decouple from environmental noise sources is highly desirable for development of quantum technologies with optimal coherence. The chemical tunability of electronic states in magnetic molecules combined with advanced electron spin resonance techniques provides excellent opportunities to address this problem. Indeed, so-called clock transitions have been shown to protect molecular spin qubits from magnetic noise, giving rise to significantly enhanced coherence. Here we conduct a spectroscopic and computational investigation of this physics, focusing on the role of the nuclear bath. Away from the clock transition, linear coupling to the nuclear degrees of freedom causes a modulation and decay of electronic coherence, as quantified via electron spin echo signals generated experimentally and in silico. Meanwhile, the effective hyperfine interaction vanishes at the clock transition, resulting in electron-nuclear decoupling and an absence of quantum information leakage to the nuclear bath, providing opportunities to characterize other decoherence sources.The ability to design quantum systems that decouple from environmental noise sources is highly desirable for development of quantum technologies with optimal coherence. The chemical tunability of electronic states in magnetic molecules combined with advanced electron spin resonance techniques provides excellent opportunities to address this problem. Indeed, so-called clock transitions have been shown to protect molecular spin qubits from magnetic noise, giving rise to significantly enhanced coherence. Here we conduct a spectroscopic and computational investigation of this physics, focusing on the role of the nuclear bath. Away from the clock transition, linear coupling to the nuclear degrees of freedom causes a modulation and decay of electronic coherence, as quantified via electron spin echo signals generated experimentally and in silico. Meanwhile, the effective hyperfine interaction vanishes at the clock transition, resulting in electron-nuclear decoupling and an absence of quantum information leakage to the nuclear bath, providing opportunities to characterize other decoherence sources.