<p>Industrial rotary angle measurement systems often employ mathematical modelling techniques for error compensation. In practice, choosing the most suitable method for systematic error modelling is important, because it directly influences overall accuracy and reliability of the system. However, comparative evaluations of different approaches remain limited. This study systematically evaluates six angular error compensation methods using a comprehensive, uncertainty-aware assessment framework. Angular deviation data was obtained from repeated cross-calibration measurements of an industrial rotary angle measurement system using a 36-sided polygon and an autocollimator. Three interpolation methods (linear, nearest-neighbor, cubic spline) and three approximation methods (polynomial, Fourier series, sum-of-sines) were evaluated using validation RMSE, information criteria, cross-validation, bootstrap robustness, Monte Carlo uncertainty propagation, and spectral analysis. Results show that linear interpolation achieves the lowest validation RMSE (0.648″) with good robustness and implementation simplicity. Among approximation methods, a fourth-degree polynomial provides the best robustness, while a three-term sum-of-sines model achieves comparable accuracy to a four-harmonic Fourier series using 56% fewer parameters and superior data robustness. Moreover, the study reveals a critical overfitting paradox: models exhibiting excellent noise smoothing can be catastrophically sensitive to calibration data selection. These findings demonstrate that bootstrap and Monte Carlo analyses quantify complementary robustness properties and are essential for reliable model selection. A comprehensive assessment framework is therefore required to ensure stable and physically meaningful error compensation in precision measurement systems.</p>