Folding and unfolding of many biological macromolecules can be characterized thermodynamically, yielding a wealth of information about the stability of various conformations and the interactions that hold them together. The relevant thermodynamic parameters are usually obtained by employing spectroscopic and/or calorimetric techniques and fitting an appropriate thermodynamic model to the experimental data. In this work, we compare the traditional approach of fitting the thermodynamic model to experimental data obtained from each experiment individually and the global approach of simultaneously fitting the model to all available data from different experiments. On the basis of several specific examples of DNA and protein unfolding, we demonstrate that piece-by-piece verification of the proposed thermodynamic model using individual fits is frequently inappropriate and can result in an incorrect mechanism and thermodynamics of the studied unfolding process. We find that while the two approaches are complementary in some aspects of analysis global fitting is essential for the appropriate selection and critical evaluation of the model mechanism. Only a good global fit thus gives us confidence that the obtained thermodynamic parameters of unfolding have real physical meaning.