With our collaborators David Ferguson and Wade DeGottardi of Northrop Grumman Corporation, we have just published in the open-access journal PRResearch a new technique for simulating large superconducting circuits. In this paper we generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert-space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization. The paper can be found here.