Two dimensional hydraulic models are useful to reconstruct maximum discharges and uncertainties of historic flood events. Since many model runs are needed to include the effects of uncertain input parameters, a sophisticated 2D model is not applicable due to computational time. Therefore, this papers studies whether a lower-fidelity model can be used instead. The presented methodological framework shows that a 1D-2D coupled model is capable of simulating maximum discharges with high accuracy in only a fraction of the calculation time needed for the high-fidelity model. Therefore, the lower-fidelity model is used to perform the sensitivity analysis. Multiple Linear Regression analysis and the computation of the Sobol’ indices are used to apportion the model output variance to the most influential input parameters. We used the 1926 flood of the Rhine river as a case study and found that the roughness of grassland areas was by far the most influential parameter.