At continental margins, energetic deep-ocean eddies can transport shelf water offshore in filaments that wrap around the eddy. One example is that of Gulf Stream warm-core rings interacting with the Mid-Atlantic Bight shelf. The rate at which shelf water is exported in these filaments is a major unknown in regional budgets of volume, heat, and salt. This unknown transport is constrained using a series of idealized primitive equation numerical experiments wherein a surface-intensified anticyclonic eddy interacts with idealized shelf–slope topography. There is no shelfbreak front in these experiments, and shelf water is tracked using a passive tracer. When anticyclones interact with shelf–slope topography, they suffer apparent intrusions of shelf–slope water, resulting in a subsurface maximum in offshore transport. The simulations help construct an approximate model for the filament of exported water that originates inshore of any given isobath. This model is then used to derive an expression for the total volume of shelf–slope water transported by the eddy across that isobath. The transport scales with water depth, radius, and azimuthal velocity scale of the eddy. The resulting expression can be used with satellite-derived eddy properties to estimate approximate real-world transports ignoring the presence of a shelfbreak front. The expression assumes that the eddy’s edge is at the shelf break, a condition not always satisfied by real eddies.