A graphene-based porous paper made of multilayer graphene (MLG) microsheets is developed for application as a flexible electrically conducting shielding material at radio frequency. The production process is based on the thermal expansion of a graphite intercalated compound, the successive liquid-phase exfoliation of the resulting expanded graphite in a proper solvent, and finally the vacuum filtration of the MLG-suspension using a nanoporous alumina membrane. Enhancement of the electrical conductivity and electromagnetic shielding properties of the MLG paper is achieved by gentle annealing at 250 °C overnight, and by mechanical compression at 5 MPa. The obtained results show that the developed MLG papers are characterized by an electrical conductivity up to 1443.2 S/cm, porosity around 43%, high flexibility, shielding effectiveness up to 55 dB at 18 GHz with a thickness of 18 μm. Numerical simulations are performed in order to understand the main factors contributing to the shielding performance of the new material.