The global stratification and circulation, and their sensitivities to changes in forcing, depend crucially on the representation of the mesoscale eddy field in a numerical ocean circulation model. Here, a geometrically informed and energetically constrained parameterization framework for mesoscale eddies — termed GEOMETRIC — is proposed and implemented in three-dimensional channel and sector models. The GEOMETRIC framework closes eddy buoyancy fluxes according to the standard Gent–McWilliams scheme, but with the eddy transfer coefficient constrained by the depth-integrated eddy energy field, provided through a prognostic eddy energy budget evolving with the mean state. It is found that coarse resolution models employing GEOMETRIC display broad agreement in the sensitivity of the circumpolar transport, meridional overturning circulation and depth-integrated eddy energy pattern to surface wind stress as compared with analogous reference calculations at eddy permitting resolutions. Notably, eddy saturation — the insensitivity of the time-mean circumpolar transport to changes in wind forcing — is found in the coarse resolution sector model. In contrast, differences in the sensitivity of the depth-integrated eddy energy are found in model calculations in the channel experiments that vary the eddy energy dissipation, attributed to the simple prognostic eddy energy equation employed. Further improvements to the GEOMETRIC framework require a shift in focus from how to close for eddy buoyancy fluxes to the representation of eddy energetics.