In this paper we report density functional theory calculations of the electronic g-tensor and hyperfine coupling constants of the copper dication in sixfold- and fivefold-coordination models of the first aqueous solvation sphere. The obtained results indicate that the electronic g-tensor of these copper complexes in combination with hyperfine coupling constants of copper in principle can be used to elucidate the coordination environment of the hydrated copper dication. In addition to these results, we have designed a methodology for accurate evaluation of electronic g-tensors and hyperfine coupling tensors in copper complexes, and demonstrate the applicability of this approach to copper dication aqua complexes.