We report a non-contact CVD graphene gas sensing method that utilises a high Q microwave dielectric resonator perturbation technique. A graphene sample is coupled to the evanescent field of a dielectric resonator whereupon nitrogen dioxide (NO2), a p-doping gas, is detected by monitoring the change in the linewidth and frequency of the resonant mode. The resonant peak shape is dependent on the number of carriers in the graphene sheet. Therefore, the linewidth perturbation can be converted to a measurement of the graphene sheet resistance. To demonstrate the strength of this technique, sensor response curves for NO2 at different concentrations and temperatures are measured showing sub ppm sensitivity. This technique eliminates interactions between the trace gas and metal contacts that otherwise effect the sensor response of the graphene device.