We report calculations of polarizabilities using total energies extrapolated to the complete basis set limit. A dual-level scheme has been employed, with the complete basis set limit of the correlation energy determined by the recently reported uniform singlet- and triplet-pair extrapolation method. The finite field approach has been employed, with tensors and averaged polarizabilities for the ground electronic states of H-2, N-2, CO, and H2O reported and compared with available experimental data in the literature. Exploratory results are also presented for C6H4NO2NH2.