The hydrologic characteristics of the 1943 outburst flood from the Glacier du Mont Miné, Switzerland, are herein reconstructed using field evidence (palaeostage indicators) in conjunction with shallow water modelling techniques. These techniques rely on accurately characterising the hydraulic roughness of the channel, the water height established as boundary conditions, and the main flow path during the former flood, but the selection of appropriate parameter values can be problematic and hence there is uncertainty in the estimated discharge. In this study, minimal flow discharge estimates derived from one-dimensional modelling were found to vary between 429 and 557 m3 s−1 as the hydraulic roughness (ks) and water height at the inlet were varied over a realistic range of values (0.8–1.4 m and 3.31–6 m, respectively), whereas flow rates derived via two-dimensional modelling were confined in a narrower, lower, range of 358–454 m3 s−1. This degree of sensitivity to bed roughness ks, boundary conditions and the spatial dimensions of the modelling approach is, for the one-dimensional modelling, higher than reported in previous studies, but the precision of flow discharge values reconstructed using the two-dimensional modelling approach appears to be acceptable, even for floods in the very steep valley (0.1 m/m) that is subject of this study.