Using millimeter-wave spectroscopy, we study the electromagnetic response of asymmetric split-ring resonators made from superconducting niobium. The asymmetry is introduced by using different arm lengths of the U-shape split-ring design. A small asymmetry allows the excitation of an otherwise dark mode with only a weak coupling to electromagnetic field. The radiation losses are strongly reduced in this geometry. The combination of weak electromagnetic coupling and reduced ohmic losses in a superconductor leads to high quality factors of split-ring resonators. Quality factors of up to 150 in an open design are achieved experimentally.