Some applications of high-temperature superconductors where their thermal radiative behavior is important, such as bolometers, optically-triggered switches and gates, and space-cooled electronics, require the superconductor to be in the form of a very thin film whose radiative behavior cannot be adequately represented by a semi-infinite analysis. Two properties of particular importance are the film absorptance and the combined film/substrate absorptance, which are crucial to the operation of many devices. Here, calculations of the absorptance of superconducting-state Y-Ba-Cu-O films on MgO substrates suggest that for film thicknesses less than about 50 nm, a decrease in the film thickness less than increase in both the film absorptance and the film/substrate absorptance. Furthermore, the film absorptance is maximum at some optimal value of film thickness. Assuming the film to be a smooth, continuous slab with a refractive index equal to that of bulk Y-Ba-Cu-O is verfied, at least in the normal state and for films as thin as 35 nm, by room-temperature reflectance and transmittance measurements.