The electron binding energies for the weak dipole-bound anions HCN- and HNC- were found to be 13.2 and 35.7 cm(-1), respectively, at the coupled cluster level of theory with single, double, and triple excitations [CCSDT]. A more approximate approach, in which the triples contribution is treated perturbatively [CCSD(T)], provides an electron binding energy which is underestimated for HCN- by 25% and overestimated for HNC- by 19%. The new results provide benchmarks for model potentials aiming to reproduce dynamical correlation effects in electron-molecule interactions.