Graphene is an attractive material for sensing applications due to its large surface-to-volume ratio and high electrical conductivity. The concentration-dependent density of states in graphene allows the capacitance in metal-oxide-graphene structures to be tunable with carrier concentration. This feature allows graphene to act as a variable capacitor (varactor). These devices have a multitude of applications, particularly for biosensing, where the small size and wireless readout are attractive features for in vivo usage. The operation of multi-finger graphene quantum capacitance varactors fabricated using a planarized local bottom gate electrode, HfO2 gate dielectric, is described. The devices show a capacitance tuning range of 1.6:1 at room-temperature, over a voltage range of ±2 V. A characterization methodology was developed to serves as a diagnostic process to ascertain graphene varactor limitations and capabilities. Since functionalization of graphene is needed to sense variety of target analytes, the material and electrical properties of graphene functionalized with glucose oxidase (GOx) was studied. The device characteristics were explored at each step of functionalization with the end goal of realizing wireless graphene glucose sensors. Finally the effect of water vapor was explored, with a demonstration of stable and reproducible wireless humidity sensor.