In transport calculations for molecular junctions based on density-functional theory, the choice of exchange and correlation functional may dramatically affect the results. In particular, local and semilocal functionals tend to overdelocalize the molecular levels, thus artificially increasing their broadening. In addition, the same molecular levels are usually misplaced with respect to the Fermi level of the electrodes. These shortfalls are reminiscent of the inability of local functionals to describe Mott-Hubbard insulators, but they can be corrected with a simple and computationally undemanding self-interaction correction scheme. We apply such a scheme, as implemented in our transport code SMEAGOL, to a variety of phenyl-based molecular junctions attached to gold electrodes. In general, the corrections reduce the current since the resonant Kohn-Sham states of the molecule are shifted away from the contact Fermi level. In contrast, when the junction is already described as insulating by local exchange and correlation potentials, the corrections are minimal and the I-V is only weakly modified.