A new Stark-type experimental technique known as electroabsorption spectroscopy has been developed in S. G. Boxer's laboratories which offers the ability to measure the responses of isotropic solvated molecules to an applied electric field. It is applicable to a wide range of molecules and environments. We present benchmark ab initio and density-functional calculations employing 14 methods and double-zeta to penta-zeta augmented basis sets for the vibrational frequencies, dipole moment, polarizability, hyperpolarizability profiles, Stark shift, and other electroabsorption properties of two important (gas-phase) molecules, CO and CN-, for which a range of high-precision experimental data is available. The results show excellent agreement with these data, verify the earlier conclusion that the transition-moment polarizability rather than the polarizability change dominates the first-derivative response in the electroabsorption spectroscopy of these systems, and convergence with respect to the treatment of electron correlation, basis set, geometrical integration, and finite-field differentiation. For large molecules, B3LYP calculations with small (eg., aug-cc-pVDZ) basis sets are predicted to offer optimum performance per computational cost.