Amorphous W/Si multilayers, with single layer thicknesses varying between 10 and 100 angstrom, have been prepared by UHV electron beam evaporation. The superconducting samples (d(W) < 30 angstrom, 3 K < T(c) < 4.2 K) are characterized by a negative temperature coefficient of the resistivity. The non-superconducting samples (d(W) > 30 angstrom) have a positive coefficient. With decreasing temperature, the parallel critical field H(c2 parallel-to)(T) shows a dimensional crossover which depends on the ratio between the total multilayer thickness and the in-plane superconducting coherence length. The amorphous character of the layers enables one to prepare continuous and smooth W layers with thicknesses down to d(W)=10 angstrom. These ultrathin layers give rise to very high values of the parallel critical fields.