The fabrication of a Nanoelectromechanical System (NEMS) capacitive switch consisting of a suspended multilayer graphene membrane, doubly clamped on a coplanar waveguide (CPW) is presented and its RF performance is evaluated. The scattering parameters are measured and compared with theory in order to assess rigorously the advantages of using multilayer graphene as a membrane for the switch. Our results show that while, in theory, graphene remains a promising candidate for NEMS applications, significant efforts are needed for improving the fabrication process of suspended graphene membranes and the quality and reproducibility of reported devices.