Because wind is one of the main forcings in storm surge, we present an idealised process-based model to study the influence of topographic variations on the frequency response of large-scale coastal basins subject to time-periodic wind forcing. Coastal basins are represented by a semi-enclosed rectangular inner region forced by wind. It is connected to an outer region (represented as an infinitely long channel) without wind forcing, which allows waves to freely propagate outward. The model solves the three-dimensional linearised shallow water equations on the f plane, forced by a spatially uniform wind field that has an arbitrary angle with respect to the along-basin direction. Turbulence is represented using a spatially uniform vertical eddy viscosity, combined with a partial slip condition at the bed. The surface elevation amplitudes, and hence the vertical profiles of the velocity, are obtained using the finite element method (FEM), extended to account for the connection to the outer region. The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end, as a function of the wind forcing frequency. In general, the results point out that adding topographic elements in the inner region (such as a topographic step, a linearly sloping bed or a parabolic cross-basin profile), causes the resonance peaks to shift in the frequency domain, through their effect on local wave speed. The Coriolis effect causes the resonance peaks associated with cross-basin modes (which without rotation only appear in the response to cross-basin wind) to emerge also in the response to along-basin wind and vice versa.