In coastal inundation simulations based on numerical solutions to the shallow water equations, faithfully representing topography and bathymetry at high enough grid resolution is known to be a crucial factor in obtaining accurate results. However, in practice, a compromise in the grid resolution is often needed to a certain level because of  constraints in computing time. As a result, a predictive capability of the model may suffer, especially in coastal inundation and recession zones. In this work, we present the implementation of subgrid techniques accounting for unresolved topography in a single layer mode of the Model Prediction Across Scales-Ocean (MPAS-O), a finite-volume based model based on staggered arbitrarily-structured C-grids. Numerical experiments using a set of test cases with wetting and drying, ranging from an idealized test problem with an analytical solution to a realistic test case of storm surge, demonstrate that the subgrid method can substantially improve the predictive capability of MPAS-O coarse-grid simulations with only a minor increase in the computing time.