Before a quantum-mechanical calculation involving electromagnetic interactions is performed, the gauge to be used in expressing the potentials must be chosen. If the calculation is done exactly, the observable results it predicts will be independent of the choice of gauge. However, in most practical calculations, approximations are made, which can destroy the gauge invariance of the predictions. We compare here the results of coupled-channel time-dependent relativistic Coulomb excitation calculations as performed in either Lorentz or Coulomb gauges. We find significant differences when the bombarding energy per nucleon is ≥2 GeV, which indicates that the common practice of relying completely on the Lorentz gauge can be dangerous.