We introduce a new approach to improve structural and dynamical determination of large metalloproteins using solid-state nuclear magnetic resonance (NMR) with H-1 detection under ultrafast magic angle spinning (MAS). The approach is based on the rapid and sensitive acquisition of an extensive set of N-15 and C-13 nuclear relaxation rates. The system on which we demonstrate these methods is the enzyme Cu, Zn superoxide dismutase (SOD), which coordinates a Cu ion available either in Cu+ (diamagnetic) or Cu2+ (paramagnetic) form. Paramagnetic relaxation enhancements are obtained from the difference in rates measured in the two forms and are employed as structural constraints for the determination of the protein structure. When added to H-1-H-1 distance restraints, they are shown to yield a twofold improvement of the precision of the structure. Site-specific order parameters and timescales of motion are obtained by a Gaussian axial fluctuation (GAF) analysis of the relaxation rates of the diamagnetic molecule, and interpreted in relation to backbone structure and metal binding. Timescales for motion are found to be in the range of the overall correlation time in solution, where internal motions characterized here would not be observable.