The equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method for general second-order properties is derived providing a quadratic, CI-like approximation and its linked form from coupled cluster (CC) energy derivative theory. The effects of the quadratic contribution, of the atomic basis set employed, and of electron correlation on NMR spin-spin coupling constant calculations using EOM-CCSD methods are investigated for a selected set of difficult molecules, notably CH3F, B2H6, CH3CN, C2H4, and CH3NH2. We find that the quadratic contribution is insignificant for the couplings in the molecules considered in this study and in addition the quadratic contribution only slightly depends on the basis set used. Therefore it seems well justified to use the less expensive CI-like approximation or its linked-diagram form to evaluate spin-spin coupling constants. The Fermi-contact contribution shows the largest variation with the change of basis sets. The diamagnetic spin-orbit (DSO) and the spin-dipole (SD) contribution vary little, seemingly being converged at the DZP level while the paramagnetic spin-orbit (PSO) term shows moderate variations. Except for very few cases, the FC contribution is dominant in all the couplings in the selected set of molecules and it is also most sensitive to the inclusion of electron correlation. The other contributions are less affected by electron correlation. Although of lesser importance, the significance of the noncontact contributions and electron correlation effects on accurate calculation of coupling constants such as (1)J((CF)-C-13-F-19) in CH3F and (1)J((CN)-C-13-N-15) in CH3CN is clearly demonstrated.