Single postdielectric resonators operating on their quasi TE011 modes were used for the measurement of the surface resistance and conductivity of graphene films grown on semi-insulating SiC substrates. With this technique the surface resistance was measured with an uncertainty of ±5% and the conductivity was evaluated with an uncertainty equal to the uncertainty in determining the film thickness. The room temperature conductivity of the graphene films proved to be in the range 5×106 to 6.4×106 S/m.