We present theoretical results for the change δG in the electrical conductance G of a mesoscopic sample due to the switching on of superconductivity. Due to competition between normal and Andreev scattering, the sign of δG depends in detail on the impurity configuration within a device. In contrast with universal conductance fluctuations, we demonstrate that δG can scale with the system size and therefore, as well as being negative, can have a magnitude much greater than 2e2/h. For clean systems, this anomalous behavior arises from low-angle quasiparticle scattering at normal-superconducting interfaces. For dirty systems it arises from the presence of normal-state conductance resonances. We also examine the magnetic-field dependence of δG and show that fields on the scale of a flux quantum through a sample can change the sign of δG and suppress its magnitude. For a superconducting order parameter of magnitude Δ0, we present results for the Δ susceptibility χΔ=limΔ0→0∂G(Δ0)/∂Δ02. For clean systems, where the normal-state conductance is quantized in units of 2e2/h, we predict that χΔ diverges at normal-state conductance steps. For dirty systems, it is shown that χΔ is sensitive to the local environment of single impurity atoms.