Abstract The onshore transport of warm Circumpolar Deep Water determines the properties of Antarctic shelf waters and drives the melting of the Antarctic ice shelves. The largest net onshore transport of CDW coincides with regions of dense water export, such as the Cape Darnley region in the East Antarctic, one of the major sources of Antarctic Bottom Water. In an eddy‐resolving regional ocean model of the Cape Darnley region, the winter downslope flow of dense water produces an eddy‐driven transport of warm modified Circumpolar Deep Water across the shelf break. At coarse resolution typical for climate models, this warm water transport is absent and needs to be parameterized. The Gent and McWilliams/Redi (GM/Redi) scheme improves the simulated hydrographic fields and recovers a transport of warm water across the shelf break. With high constant GM/Redi coefficients that improve the mean hydrography the most, however, the on‐shelf transport of warm water is overestimated. This is because the dynamical suppression of eddy‐driven transports across sloping bottom topography is not considered in the GM/Redi scheme. Therefore, we implement a topography‐aware version of the GM/Redi scheme that reduces the coefficients over steep continental slopes, representing the eddy‐suppressive effect of sloping bottom topography. The topography‐aware GM/Redi scheme outperforms the traditional version by simultaneously improving the mean hydrographic fields and the cross‐slope warm water transports. Eddy parameterizations remain important for the representation of onshore tracer transports and shelf water masses in ocean models provided they incorporate regional and local physics as in our example of a topography‐aware scheme. Plain Language Summary Eddies—ocean whirls with length scales of tens to hundreds of kilometers—transport warm water across the Antarctic continental slope and onto the shelf, where they contribute to the melting of Antarctic ice masses. In a high‐resolution regional model of the Cape Darnley region in East Antarctica, eddies form when dense water flows from the shelf into the deep ocean. These eddies then carry warm water shoreward across the shelf break. However, in coarse‐resolution climate models, eddies are not resolved, resulting in the absence of warm water transport toward the shelf. To address this, we activate an additional scheme in the model that represents eddy fluxes at coarse resolution. This scheme can restore the missing transport and is most effective when it accounts for the slope of the ocean floor. Key Points In a regional ocean model, the downslope flow of dense water in the Cape Darnley region produces an eddy‐driven onshore warm water transport At coarse resolution, the onshore transport of warm water is absent but can be restored by employing a classical eddy parameterization The parameterization is most effective when it is modified to consider the suppressive effect of sloping bottom topography