Neutral (l-histidinato)(l-glutaminato)copper(II) [Cu(His)(Gln)] has been established as the most abundant ternary copper(II) amino acid compound of the exchangeable copper(II) pool in blood plasma. The experimental studies of Cu(His)(Gln) and bis(glutaminato)copper(II) [Cu(Gln)2] in solutions did not specify their complete geometries. To determine the geometries, this paper investigates the conformers, energy landscapes, and a structure–magnetic parameters relation of Cu(Gln)2 and Cu(His)(Gln) by the density functional theory (DFT) calculations. We assume a glycine-like coordination of Gln (other coordination patterns are dismissed because of steric reasons), and three His in-plane copper(II) binding modes. The conformational analyses are performed in the gas phase and implicitly modeled aqueous solution. The reliability of the DFT relative electronic and Gibbs free energies of the Cu(His)(Gln) conformers is confirmed by benchmarking against the corresponding energies obtained by the domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. Several cis- and trans-Cu(His)(Gln) conformers with His in the histaminate-like and glycine-like modes have low Gibbs free energies, and the greatest estimated metal-binding affinities. The DFT-calculated magnetic parameters of the low-energy conformers reproduce best the experimental electron paramagnetic resonance parameters measured in aqueous solutions for trans- and cis-Cu(Gln)2 conformers having two oxygen atoms (either from Gln or water molecules) at the apical positions, and Cu(His)(Gln) conformers having His in the histaminate-like mode with an apically placed carboxylato oxygen atom. The predicted conformational flexibility of His‑copper(II)-amino acid compounds may be connected with their physiological abundance, and the role in copper(II) exchange reactions in blood plasma.