In this work the groundwork is laid for characterizing the mobility of hydrogen-hydrogen pairs (proton-proton radial vectors) in proteins in the solid state that contain only residual water. In this novel approach, we introduce new ways of analyzing and interpreting data: 1) by representing hydrogen mobility (HM) and melting diagram (MD) data recorded by wide-line 1 H NMR spectroscopic analysis as a function of fundamental temperature (thermal excitation energy); 2) by suggesting a novel mode of interpretation of these parameters that sheds light on details of protein-water interactions, such as the exact amount of water molecules and the distribution of barrier potentials pertaining to their rotational and surface translational mobility; 3) by relying on directly determined physical observables. We illustrate the power of this approach by studying the behavior of two proteins, the structured enzyme lysozyme and the intrinsically disordered ERD14.