The surface resistance of Ag, Au and A1 thin conducting films deposited on low loss dielectric substrates at microwave frequencies using TE011 mode single post-dielectric resonator (10-13.22 GHz) was measured to calculate their conductivity in relation to layers thickness. This method enabling measurements near metal-insulator percolation transition was also applied for epitaxial graphene deposited on semi-insulating SiC. Moreover, effective microwave conductivity has been determined for intentionally made aluminum island structure where the DC conductivity is equal to zero. Special attention was paid to films thickness measurements which is critical for accuracy of sheet resistance calculation. Conductivity of thin metal layers and very thin graphene was compared.