Metallic point contacts were investigated at very low temperatures down to 50 mK using a piezoelectric stepping motor for the adjustment of these point contacts in a dilution refrigerator, Conductance fluctuations are observed in the magnetoresistance of pressure-type Ag-Ag point contacts, The voltage dependence of the fluctuation pattern is analyzed in view of the energy-dependent ballistic transport of the conduction electrons through the contact. Andreev reflection is observed in the current-voltage characteristics of point contacts between the normal metal Ag and the heavy-fermion superconductor UPt3. The comparison of structures in the differential resistance of a Ag-UPt3 point contact as a function of voltage with those for a conventional isotropic superconductor points to an anisotropic superconducting order parameter for UPt3.