We report on the investigation of the effects of the nonlinear inductance of huge Josephson junction arrays on high-quality RF circuits. The inductance of a single junction is far too small for use in many RF applications; however, Josephson junction stacks and especially intrinsic Josephson junctions in crystalline-layered superconductors open new opportunities. The stack inductance can be altered by changing a DC Josephson current either using an external bias current or an external magnetic field applied to a closed superconducting loop containing two stacks connected in parallel. Using stacks of Josephson junctions in the LC resonators, a tunable 4-pole, 15 MHz band-pass filter with a centre frequency at 1.1 GHz was designed. The filter was simulated in the time domain and the response was converted to the frequency domain. It was found that using an input power level of −62 dBm, corresponding to 0.5% of the junctions’ critical current, a linear approximation for the stack nonlinear inductance can be used. By changing the applied magnetic field, a tuning range of 20% was demonstrated with a tuning speed of 2 µs or better. An estimate of the losses is also given. In addition, power handling up to −26 dBm is reported using increasing circuit complexity.