In our continuing effort to identify NMR spin-spin coupling constants as fingerprints for hydrogen bond type and use these to obtain structural information, EOM-CCSD calculations have been performed to determine one-bond ((1d)J(H-H)) and three-bond ((3d)J(X-M)) spin-spin coupling constants across X-(HH)-H-...-M dihydrogen bonds for complexes with C-13-H-1, N-15-H-1, and O-17-H-1 proton-donor groups and proton-acceptor metal hydrides Li-7-H-1 and Na-23-H-1. Unlike two-bond spin-spin coupling constants across N-H-N, N-H-O, O-H-O, and Cl-H-N hydrogen bonds that are determined solely by the Fermi-contact term, (1d)J(H-H) receives nonnegligible contributions from the paramagnetic spin-orbit and diamagnetic spin-orbit terms. However, these terms tend to cancel, so that the curve for the distance dependence of (1d)J(H-H) is determined by the distance dependence of the Fermi-contact term. The value of (1d)J(H-H) is dependent on the nature of the proton donor and proton acceptor, and the relative orientation of the bonded pair. Hence, it would be difficult to extract structural information from experimentally measured coupling constants unless EOM-CCSD calculations were performed on a model complex that closely resembles the experimental complex. (3d)J(C-Li) values for the equilibrium structures of seven linear complexes stabilized by C-(HH)-H-...-Li bonds are dependent on C-Li distances, and are also sensitive to structural changes which remove any one of these four atoms from the dihydrogen bond. (3d)J(O-M) for the complexes HOH:HLi and HOH:HNa exhibit unusual behavior as a function of the O-M distance, increasing with increasing distance through a change of sign, reaching a maximum, and then subsequently decreasing.