A zero‐frequency bridge has been developed for measuring the inductance and the current‐vs‐quantum‐phase relation of superconductors. The current null detector is a SQUID magnetometer coupled to the bridge by a superconducting transformer. The bridge is balanced by adjusting precision resistors at room temperature. The theory of the bridge and analysis of the null‐detector circuit for optimizing the sensitivity are given. For current‐dependent inductors, a definition of inductance based on the quantum‐phase difference is shown to be useful. Construction and operation of the bridge are described and measurements of inductance vs temperature for Al thin‐film meander lines are presented. Zero‐frequency measurements avoid the stray coupling to capacitances and normal metal inductances found in high‐frequency measurements and the method could give high‐precision absolute measurements. The sensitivity of the present instrument is such that an inductor of 4×10−7H was measured to a relative precision of one part in 104with a measuring current of 5×10−6A. Considerable improvement is possible, especially for circuit elements of very small inductance such as Josephson junctions and weak‐link superconductors.