  We theoretically investigate the simulation of moving cavities in a
superconducting circuit setup. In particular, we consider a recently proposed
experimental scenario where the phase of the cavity field is used as a moving
clock. By computing the error made when simulating the cavity trajectory with
SQUIDs, we identify parameter regimes where the correspondence holds, and where
time dilation, as well as corrections due to clock size and particle creation
coefficients, are observable. These findings may serve as a guideline when
performing experiments on simulation of moving cavities in superconducting
circuits.
