Using Curl's Hamiltonian (Curl, R. F. Mol. Phys. 1965, 9, 585) first-principles calculations at the Hartree-Fock and various coupled-cluster (CC) levels based on a perturbative scheme are reported. The effects of basis-set dependence and electron correlation have been investigated by performing benchmark calculations for a set of radicals comprising 12 species and 14 electronic states. In comparison to experimental results, the electron spin-rotation tensor is obtained with a 10-15% accuracy when using the CC singles and doubles approximation and a triple-zeta quality basis set. Some improvements are seen when triple excitations are considered via the CC singles, doubles, and triples model.