Freestanding silicon nitride membranes with thicknesses down to a few tens of nanometers find use as TEM windows or soft X-ray spectral purity filters. As the thickness of a membrane decreases, emissivity vanishes, which limits radiative heat emission and resistance to heat loads. We show that thin metal layers with thicknesses in the order of 1 nm enhance the emissivity of thin membranes by two to three orders of magnitude close to the theoretical limit of 0.5. This considerably increases thermal load capacity of membranes in vacuum environments. Our experimental results are in line with classical theory in which we adapt thickness dependent scattering terms in the Drude and Lorentzoscillators.