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In this paper, we present a computational procedure that utilizes real-space grids to obtain high precision approximations of electrostatically confined few-electron states such as those that arise in gated semiconductor quantum dots. We use the full configuration interaction method with a continuously adapted orthonormal orbital basis to approximate the ground and excited states of such systems. We also introduce a benchmark problem based on a realistic analytical electrostatic potential for quantum dot devices. We show that our approach leads to highly precise computed energies and energy differences over a wide range of model parameters. The analytic definition of the benchmark allows for a collection of tests that are easily replicated, thus facilitating comparisons with other computational approaches. [ABSTRACT FROM AUTHOR]