The miniaturization of mechanical components with complex shapes is a great challenge in emerging applications. Silicon nitride (Si3N4) ceramics are excellent candidates for such applications due to their outstanding mechanical, thermal, and tribological properties. However, they are difficult to machine using normal mechanical machining methods. If the material were electrically conductive, electrical discharge machining (EDM) could be applied to produce precise and complex shapes. In this paper, in order to investigate the effects of electrical conductivity on the EDM characteristics, several carbon nanostructure composite materials are fabricated and EDMed using the assisting electrode method proposed by the current authors. The performance of the process is evaluated as a function of the carbon nanostructure content and type. The former is separately selected to be close to the electrical percolation threshold (0.9 vol.% and 5.3 vol.% for carbon nanotube (CNT) and graphene Nano platelet (GNP) composites, respectively), and well above that limit (5.3 vol.% and 20.6 vol.%), where electrical conductivities on the order of 10 and 100 S·m-1 are attained for CNTs and GNPs-based nanocomposites, respectively. In addition, bare Si3N4 specimens are also tested. Material removal rate, electrode wear ratio, and surface roughness of the machined pieces are analyzed for all testing conditions.