We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in early numerical methods, whereas they are employed to an increasing extent in state of the art computational fluid dynamics codes, in combination with high-order methods, such as the Finite Element Method and the Spectral Element Method. Here we consider a specific Discontinuous Galerkin (DG) method implemented in the framework of the deal.II library, which natively supports high-order mappings. A number of numerical experiments based on classical benchmarks over idealized orographic profiles demonstrate the positive impact of curved boundaries on the accuracy of the results, with no significantly adverse effect on the computational cost of the simulation. These findings are also supported by results of the application of this approach to non-smooth and realistic orographic profiles.