The invention relates to a system for measuring magnetic flows. Said system comprises a substrate which has a high dielectric constant and is placed between the SQUID and the reading loop. Advantageously, the substrate consists of SrTi03 having a dielectric constant epsilon of approximately 2000 at a temperature of 77 K. Said substrate thus acts as a resonator which advantageously absorbs the radiated rf-energy. The operating point of the SQUID is significantly more stable than in a corresponding coplanar system, and the sensitivity reached of the HTSL-SQUID is advantageously increased.