  We study gauge dependence of gravitational waves produced from a first-order
phase transition in classical scale-invariant $U(1)'$ models. Accidental gauge
independence of the one-loop effective potential in this class of models is
spoiled by including thermal resummation. The gauge artifact in the resummed
effective potential propagates to the gravitational wave spectrum and results
in one order of magnitude uncertainties in the prediction under a specific
gauge choice.
