I think he wants only a box and not an entire room; I guess it would be ok to have a metal box with proper metal mesh gasket shielding.
Depènding on the frequency, even a small, microscopic aperture, will make the signal enter in the box. I'm talking of a small space, in GHz range, even a sheet of paper between the cover and the box it's an enter point.
The matter is to minimize the reflections, because otherwise the signal you measure could be the signal + many reflections... rf adsorbing material are really expensive.