The sensitivities to measurement errors and potential effectiveness of six methods (involving reflection, emission, and ellipsometry) for determining the optical constants (index of refraction n and extinction coefficient k) of isotropic conductors are compared. The methods treated are generally regarded as most promising for use with high-temperature solid and liquid metals with smooth surfaces of high purity. For each method, contours of constant measured variable are plotted vs n and k. By analysis of the spacing and angle of intersection of these contours, we show that only methods based on measuring both amplitude attenuation and phase shift on reflection can yield n and k, and thus the spectral and directional emissivity, reflectivity, and absorptivity, with reasonable precision over the spectral range 0.4 to 10 mum. Methods based only on amplitude attenuation on reflection, or on the angular dependence of emission, are poorly suited to ranges of n and k that are typical of the infrared. The method of Beattie and Conn retains the ability to determine both optical constants to 10 mum.