The development of scalable, on-chip multiplexing technology, capable of electrically characterising an array of nanomaterial field-effect transistors at cryogenic temperatures, is described. The channel in each transistor in the array is a nanomaterial which is transferred onto the multiplexer device, and each transistor in the array can be measured individually. The underlying multiplexer device is fabricated from a GaAs / AlxGa1−xAs heterostructure; nanomaterials successfully incorporated into the multiplexer circuit are monolayer graphene and InAs nanowires. Two device designs are presented: the first can characterise up to 16 field-effect transistors; the second, up to 128. A 16-output multiplexer, with 11 functioning graphene field-effect transistors is the primary focus of this thesis. This device is characterised by multiple magneto-transport experiments, which demonstrate that the multiplexing technique can be used to collect reproducible data that is consistent with existing results, at a rate higher than what would otherwise be possible. In the absence of a magnetic field, transistors are characterised by calculating commonly used metrics, such as the carrier mobility and the intrinsic carrier density, which are found to be consistent over multiple device cool-downs. In weak magnetic fields, the scattering processes are investigated by analysing weak localisation signals and reproducible conductance fluctuations. In strong magnetic fields, Landau quantisation is observed in some of the graphene channels. The level spacing is used to calculate the Fermi velocity of carriers and the cyclotron mass of carriers in each Landau level, which provides conclusive evidence that the intrinsic properties of graphene are not significantly altered by the multiplexing technique. From the magneto-transport experiments, it is evident that many-body electron interactions are relevant to the observed transport phenomena. At low temperature and strong magnetic field, a transition into an insulating state is observed in one of the channels, which also is likely to be caused by many-body effects. Finally, initial results from ongoing work are presented, which includes extending the device design so that it can operate at both room temperature and cryogenic temperature, and the measurement of InAs nanowire field-effect transistors.