A robust method that uses eddy current measurements to determine the conductivity and thickness of uniform conductive layers is described. The method was tested by estimating the conductivity and thickness of aluminum and copper layers on various substrate metals, and the thickness and conductivity of free-standing foils of aluminum. The electrical impedance was measured for air-core and ferrite-core coils in the presence and absence of the layer for frequencies ranging from 1 kHz to 1 MHz. The thickness and conductivity of the metal layers were inferred by comparing the data taken with air-core coils to the exact theoretical solution of Dodd and Deeds [J. Appl. Phys. 39, 2829 (1968)] using a least-squares norm. The inferences were absolute in the sense that no calibration was used. We report experimental tests for eight different thicknesses of aluminum (20-500-mu-m) in free space and on four different substrates: Ti-6Al-4V, 304 stainless steel, copper, and 7075 aluminum, and for five different thicknesses of copper (100-500-mu-m) on 304 stainless steel. Both the thickness and conductivity could be determined accurately (typically within 10%) and simultaneously if the ratio of the layer thickness to the coil radius was between 0.20 and 0.50. For thinner samples either the thickness could be found if the conductivity were known, or vice versa.