The concept involved here is Emissivity - the ability to emit energy. e is the usual symbol, and a perfect emitter would have an e of 1. Your perfect black body will have this emissivity of 1.
A highly polished surface (polished at all the wavelengths concerned) will have an emissivity much smaller. Polished silver has an emissivity of about 0.02.
In general the emissivity of a surface is inversely related to its reflectance, but this does vary with the surface finish, colour, and the mass of the object.
It is worth noting, that low emissivity glass is used with effect in the double glazing of windows.