Atom-based standards for length and time as well as other physical quantities such as magnetic fields show clear advantages by enabling stable and uniform measurements. Here we demonstrate a new method for measuring microwave (MW) electric fields based on quantum interference in a rubidium atom. Using a bright resonance prepared within an electromagnetically induced transparency window we could achieve a sensitivity of ~30μVcm-1Hz-1/2 and demonstrate detection of MW electric fields as small as ~8μVcm-1 with a modest set-up. The sensitivity is limited, at present, by the stability of our lasers and can be significantly improved in the future. Our method can serve as a new atom-based traceable standard for MW electrometry, with its reproducibility, accuracy and stability promising advances towards levels comparable with those attained in magnetometry at present.