Barotropic tide models are single-layer, shallow water models forced by an oscillatory body force at the tidal frequency. They are widely used in a variety of applications at increasingly high spatial resolutions to take advantage of new high-resolution bathymetric datasets. Here, we investigate the impact of the small-scale roughness present in such bathymetry on the solutions obtained by these models. It is shown that rough topography induces a form stress that scales with the depth variance relative to the mean depth and is out of phase with the tidal flow. As such, this force extracts no energy from the tide but can significantly damp or amplify tidal elevations depending on the resonant properties of the basin. Due to these effects, barotropic tidal models only converge with increasing resolution once the variance of the topography is fully represented. These results have important implications for improving the accuracy of barotropic tide models.