Both ocean process and prediction studies increasingly rely on state estimation (i.e., data assimilation) to provide the most complete representation of how the ocean circulates. This study applies the formalism and methodology of state estimation, recently developed for the global, coarse-resolution problem, to eddy-permitting state estimation in regional domains. Two major challenges exist for a state estimate that is nested inside a global state estimate: (1) estimation of open-boundary conditions consistent with information interior and exterior to the regional domain and (2) estimation with the higher-resolution models of regional studies. Here a least squares cost function defines the problem of minimizing the misfit between a North Atlantic regional general circulation model and actual observations, including those of the Subduction Experiment. A first experiment, using a novel "multiscale" method to constrain the large-scale regional circulation, shows that the use of the adjoint of both an eddy-permitting model and its coarse-resolution twin leads to a solution of the least squares problem in a computationally practical way. Therefore no fundamental obstacle exists to constraining the large-scale regional circulation nested within a global circulation. A second experiment in the North Atlantic shows that the model circulation can be constrained to the full observational signal, including eddy variability, as observed at selected point locations. Both experiments in this study produce eddy-permitting state estimates which are exactly self-consistent with the equations of motion as embodied by a general circulation model. Therefore dynamical balances can be diagnosed and easily interpreted; in particular, a companion paper uses the state estimates to determine eddy subduction rates in the North Atlantic.