The Bose-Hubbard model is central to the study of strongly-correlated bosonic systems and finds implementation using either arrays of Josephson junctions, or ultra-cold bosonic atoms trapped in optical lattices. For Josephson junction arrays, the constituent bosons are charged, the Coulomb interaction extends over many sites, and the system can be probed by electrical transport measurements. There is also an intimate connection between one-dimensional chains of Josephson junctions, and one-dimensional superconducting nanowires, where the Coulomb blockade of Cooper pair tunnelling (or alternatively, coherent quantum phase slips of the superconducting order parameter), should lead to an electromagnetic “dual” to the conventional Josephson effect. Such a dual Josephson effect exhibits a critical voltage, in contrast to a critical supercurrent, which arises since charge is localised and global phase coherence is absent. We have measured the critical voltage for a statistically large number of one-dimensional, single-junction chains of Josephson junctions, where we have varied the ratio of Josephson to charging energies and the plasma frequency, using respectively, geometry and barrier thickness. We observe universal scaling of the critical voltage with the singlejunction Bloch bandwidth. The power-law exponent does not agree with theory based on semi-classical treatment of junction quasicharge (the charge which has passed through a given junction). In addition, we have recently extended our measurements to SQUID chains, finding additional and unexpected surprises.