Two-dimensional materials offer a novel platform for the development of future quantum technologies. However, the electrical characterisation of topological insulating states, non-local resistance, and bandgap tuning in atomically thin materials can be strongly affected by spurious signals arising from the measuring electronics. Common-mode voltages, dielectric leakage in the coaxial cables, and the limited input impedance of alternate-current amplifiers can mask the true nature of such high-impedance states. Here, we present an optical isolator circuit which grants access to such states by electrically decoupling the current-injection from the voltage-sensing circuitry. We benchmark our apparatus against two state-of-the-art measurements: the non-local resistance of a graphene Hall bar and the transfer characteristic of a WS2 field-effect transistor. Our system allows the quick characterisation of novel insulating states in two-dimensional materials with potential applications in future quantum technologies.