A method of characterizing a tunable superconducting circuit, includes selecting an operating direct current (DC) flux for a first charge island from a plurality of coupled charge islands residing in the tunable superconducting circuit coupled to a first resonator and a second resonator, tuning operating DC flux values for at least two charge islands from the plurality of coupled charge islands, measuring coupling energies of the first resonator and the second resonator and measuring frequencies from each of the plurality of coupled charge islands.