The dependence of the conductance of ballistic wires on the work function of different metals is analyzed. We show that quantum finite-size effects can be taken into account by a simple correction to the Sharvin formula. Although the conductance is suppressed relative to the classical Sharvin limit, the correction is much smaller than that obtained from calculations based on ``hard-wall'' boundary conditions. Different sources of errors in the determination of actual cross sections in atomic-scale contacts from conductance measurements are discussed.