Electromagnetic interference shielding structure including carbon nanotube or nanofiber films

A composite material for electromagnetic interference shielding is provided. The composite material comprises a stack including at least two electrically conductive nanoscale fiber films, which are spaced apart from one another by at least one insulating gap positioned between the at least two nanoscale fiber films. The stack is effective to provide a substantial multiple internal reflection effect. An electromagnetic interference shielded apparatus and a method for shielding an electrical circuit from electromagnetic interference is provided.