Graphene nanoplatelets (GNPs)/epoxy composites have been fabricated via gravity molding. The electrical and thermal properties of the composites have been studied with variable GNP type (C300, C500, and C750, whose surface areas are ~300, 500, and 750 m2/g, respectively), GNP loading (5, 10, 12, and 15 wt.%), and dispersion time via ultrasonication (0, 30, 60, and 120 min). By increasing the time of sonication of the GNP into the epoxy matrix, the electrical conductivity decreases, which is an effect of GNP fragmentation. The best results were observed with 10–12% loading and a higher surface area (C750), as they provide higher electrical conductivity, thereby preserving thermal conductivity. The influence of sonication over electrical conductivity was further analyzed via the study of the composite morphology by means of Raman spectroscopy and X-ray diffraction (XRD), providing information about the aspect ratio of GNPs. Moreover, electromagnetic shielding (EMI) has been studied up to 4 GHz. Composites with C750 and 120 min ultrasonication show the best performance in EMI shielding, influenced by their higher electrical conductivity.