•Simulation of appendix gap losses is very sensitive to energy transport assumptions.•Available empirical approaches lack a sufficient theoretical and experimental basis.•Enhanced correlations are derived on the basis of an unsteady analytical flow model.•High-resolution gas temperature measurements in the gap confirm its predictions.•Discrepancies between analytical and numerical loss predictions could be resolved. Regenerative machines, such as the Stirling engine, may contribute substantially to the solution of the present environmental problems, if they are designed for high efficiency. This requires a thorough understanding and an accurate modelling of the various losses, including the so-called appendix gap loss. For this purpose, some analytical models as well as a few one-dimensional numerical approaches have been developed so far. In this contribution, a comparison of the results obtained by these is performed for the reference case of a well-documented experimental machine. It reveals significant discrepancies regarding the optimum gap width as well as the magnitude of the loss. Particularly for large gap widths, increasing deviations between the analytical and the numerical models are observed. The latter even predict an unrealistic maximum. This discrepancy can be resolved by additionally considering the p,V-work done by the moving seal. Further deviations at small gap widths can be attributed to the interdependence of the loss and the actual wall temperature gradients, which is included in the numerical models. Instead, a preset value is assumed in the analytical models. This also applies to a newly developed, enhanced model, which predicts the optimum width reliably, but overestimates the magnitude of the loss throughout. This underlines a need for one-dimensional differential simulations in addition to analytical modeling. However, these require separate modeling approaches for both the radial and axial energy transport. Unfortunately, the choice of these significantly affects the results. Since none of the approaches proposed so far is theoretically or experimentally founded, there is no basis for a correct choice. To solve this problem, the aforementioned analytical model is considered, since it is theoretically based and further supported by recent experimental results presented in this contribution. It is therefore used to analytically derive correlations for the phase-shifted heat exchange with the walls and the interrelation of enthalpy and mass flow. Thus, a theoretically and experimentally founded reference model is available now. Comparing the results obtained by this reference model and the other numerical approaches, it is found that an empirical model based on the assumption of parabolic radial temperature profiles and ideal plug flow yields almost the same results as the former. Since this model is easier to use, it can therefore be recommended for general practical use. The reference model may, however, be used for countercheck purposes and for further optimization work.