Very high currents can be induced in pairs of current-carrying superconducting rings when they are coaxially brought closer. If the currents are uniformly distributed through the cross-section of the rings their magnitude can be derived from the mutual inductance of interacting rings. However, if the currents are not uniformly distributed that calculation procedure should be no longer applicable. The aim of this paper is to report on an alternative procedure to determine the induced currents by measuring the magnetic flux density around the rings and applying the Ampre’s circuital law. Our results show that in axially confronted rings the induced currents may be significantly larger than the critical current of an isolated ring, which may be explained in terms of a reduction of the magnetic self-field.