Using X-band pulsed electron-spin resonance, we report the intrinsic spin-lattice (T1) and phase-coherence (T2) relaxation times in molecular nanomagnets for the first time. In Cr7M heterometallic wheels, with M=Ni and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the molecule. In deuterated samples T2 reaches 3 micros at low temperatures, which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of molecular nanomagnets in quantum information applications.