The electromagnetic shielding of an enclosable building structure is provided by applying a shielded covering to overlay optical openings in the building structure. The shielded covering comprises a metal-coated woven substrate and a shielding coupling. The metal-coated woven substrate has a woven substrate and a metal coating. The woven substrate may be organic and comprise threads of intermingled fibers such as silk fibers. The metal-coated woven substrate may also have a protection feature such as transparent resin, of barriers of glass or transparent polymeric material. The shielded coupling connects the shielded covering to other shielding components of a shielded building structure to preserve shielding continuity over the interface between shielding components.