We report on the experimental study of electromagnetic (EM) properties of multilayered graphene in K(a)-band synthesized by catalytic chemical vapor deposition (CVD) process in between nanometrically thin Cu catalyst film and dielectric (SiO2) substrate. The quality of the produced multilayered graphene samples was monitored by Raman spectroscopy. The thickness of graphene films was controlled by atomic force microscopy (AFM) and was found to be a few nanometers (up to 5 nm). We discovered, that the fabricated graphene, being only some thousandth of skin depth, provided remarkably high EM shielding efficiency caused by absorption losses at the level of 35-43% of incident power. Being highly conductive at room temperature, multilayer graphene emerges as a promising material for manufacturing ultrathin microwave coatings to be used in aerospace applications.