A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.