Understanding the thermodynamic signature of protein-peptide binding events is a major challenge in computational chemistry. The complexity generated by both components possessing many degrees of freedom poses a significant issue for methods that attempt to directly compute the enthalpic contribution to binding. Indeed, the prevailing assumption has been that the errors associated with such approaches would be too large for them to be meaningful. Nevertheless, we currently have no indication of how well the present methods would perform in terms of predicting the enthalpy of binding for protein-peptide complexes. To that end, we carefully assembled and curated a set of 11 protein-peptide complexes where there is structural and isothermal titration calorimetry data available and then computed the absolute enthalpy of binding. The initial "out of the box" calculations were, as expected, very modest in terms of agreement with the experiment. However, careful inspection of the outliers allows for the identification of key sampling problems such as distinct conformations of peptide termini not being sampled or suboptimal cofactor parameters. Additional simulations guided by these aspects can lead to a respectable correlation with isothermal titration calorimetry (ITC) experiments (R2 of 0.88 and an RMSE of 1.48 kcal/mol overall). Although one cannot know prospectively whether computed ITC values will be correct or not, this work shows that if experimental ITC data are available, then this in conjunction with computed ITC, can be used as a tool to know if the ensemble being simulated is representative of the true ensemble or not. That is important for allowing the correct interpretation of the detailed dynamics of the system with respect to the measured enthalpy. The results also suggest that computational calorimetry is becoming increasingly feasible. We provide the data set as a resource for the community, which could be used as a benchmark to help further progress in this area.