  We present numerical calculations of the conductance of an interface between
a phase-coherent two-dimensional electron gas and a superconductor with a
quantum point contact in the normal region. Using a scattering matrix approach
we reconsider the geometry of De Raedt, Michielsen, and Klapwijk [Phys. Rev. B,
50, 631 (1994)] which was studied within the time-dependent Bogoliubov-de
Gennes formalism. We find that the factor-of-two enhancement of the conductance
G_NS compared to the normal state conductance G_N for ideal interfaces may be
suppressed for interfaces with a quantum point contact with only a few
propagating modes. The suppression is found to depend strongly on the position
of the Fermi level. We also study the suppression due to a barrier at the
interface and find an anomalous behavior caused by quasiparticle interference.
Finally, we consider the limit of sequential tunneling and find a suppression
of the factor-of-two enhancement which may explain the absence of conductance
enhancement in experiments on metal-superconductor structures.
