Using multireference configuration interaction methods, the potential energy curves of the ground and several low-lying excited states of the NO+ ion were calculated. We obtain spectroscopic parameters in good agreement with existing experimental data. In order to establish a one-to-one correspondence between the experimentally known term energies of the recently detected b 3PI-->a 3SIGMA+, transition [Huber and Vervloet, J. Mol. Spectrosc. 146, 188 (1991)] and ab initio data, it is necessary to include explicitly spin-orbit and rotational coupling. Spin-orbit matrix elements were evaluated using the microscopic Breit-Pauli Hamiltonian. The off-diagonal coupling matrix elements [b 3PIH(SO)a 3SIGMA+] and [b 3SIGMALa 3SIGMA+] are found to depend strongly on the internuclear separation. The calculated vibrationally averaged fine structure parameter of the b 3PI state for upsilon = 0 (67.21 cm-1) is found to be in very good agreement with the value determined experimentally (69.699 cm-1).