  The scattering of vortices at a critical value of the coupling constant in
the Lagrangian can be approximated by a geodesic motion in the moduli space of
classical static configurations of vortices. In this paper we give a scheme for
generalising this idea to couplings that are near to the critical value. By
perturbing a critically coupled field, we show that scattering of vortices at
near-critical coupling can be approximated by motion in the original moduli
space with a perturbed metric, and a potential. We apply this method to the
scattering of two vortices, and compare our results to recent numerical
simulations, and find good agreement where the scattering is not highly
sensitive to radiation into other field modes. We also investigate the
possibility of bound stable orbits of two vortices in the quantum field theory.
