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The aim of this research is to measure the dielectric properties and electromagnetic interference (EMI) shielding effectiveness (SE) of silicone rubber reinforced with graphene nanoplates. In a two-roll mill, different amounts of graphene are mixed together. This is followed by compression moulding at 170°C and post-curing for 4 h at 200°C. Between 1 MHz and 1 GHz, the waveguide transmission line method and a vector network analyser are used to measure the dielectric and EMI SE parameters. As the amount of graphene is increased from 0 to 7 wt%, AC conductivity goes up, reaching 1.19 × 10−3 S/cm at 7 wt%. The same composition gives the highest EMI SE of 43.22 dB at 1 GHz. The high-frequency structural simulation of different compositions shows how shielding works, and the results agree with what has been seen in experiments.