We show how to characterize the native-structure models of a protein using our free-energy function F which is based on hydration thermodynamics. Ubiquitin is adopted as an example protein. We consider models determined by the X-ray crystallography and two types of NMR model sets. A model set of type 1 comprises candidate models for a fixed native structure, and that of type 2 forms an ensemble of structures representing the structural variability of the native state. In general, the X-ray models give lower F than the NMR models. There is a trend that, as a model deviates more from the model with the lowest F among the X-ray models, its F becomes higher. Model sets of type 1 and those of type 2, respectively, exhibit two different characteristics with respect to the correlation between the deviation and F. It is argued that the total amount of constraints such as NOEs effectively taken into account in constructing the NMR models can be examined by analyzing the behavior of F. We investigate structural characteristics of the models in terms of the energetic and entropic components of F which are relevant to intramolecular hydrogen bonding and to backbone and side-chain packing, respectively.