Trap circuits for use with superconducting integrated circuits having capacitively-coupled resonant clock networks are described. An example superconducting integrated circuit (IC) includes a clock structure coupled: (1) to a first Josephson junction (JJ) via a first capacitor, where the first capacitor is configured to receive a clock signal via the clock structure and couple a first bias current to the first JJ, and (2) to a second JJ via a second capacitor, where the second capacitor is configured to receive a clock signal via the clock structure and couple a second bias current to the second JJ. The superconducting IC further includes a trap circuit coupled between the first capacitor and the first JJ, where the trap circuit is configured to attenuate any signals generated by a triggering of the first JJ to reduce crosstalk between the first JJ and the second JJ.