Present day climate models employ a coarse horizontal grid that is unable to fully resolve estuaries or continental shelves. The importation of fresh water from rivers is critical to the state of deep ocean stratification, but currently the processing of that fresh water as it passes from the river through the estuary and adjacent shelf is not represented in the coastal boundary conditions of climate models. An efficient way to represent this input of fresh water to the deep ocean would be to treat the estuary and shelf domains as two coupled box models with river water input to the estuarine box and mixed fresh water and coastal water output from the shelf box to the deep ocean.We develop and test the estuary box model here. The potential energy anomaly ϕ is found from the five competing rates of change induced by freshwater inflow, mixed water outflow to the shelf, tidal mixing, surface heat flux, and wind-induced mixing. When application of the box model is made to the Delaware estuary, the wind mixing term contributes little. A 15-year time series of ϕ compares surprisingly well with the calculations of a three-dimensional numerical model applied to the Delaware estuary. The results encourage the future development of a shelf box model as the next step in constructing needed boundary conditions for input of fresh water to the deep ocean component of coupled climate models.