The problem of an electromagnetic wave packet, incident on a relativistically moving plane ionization or recombination front in a stationary gas, is considered. The frequency of the reflected wave packet is found to obey the usual double Doppler shift relation. However, the reflection coefficients and the physics can differ significantly from the case of reflection from moving material objects. In the unmagnetized case, the ratio of the energy in the reflected wave packet to that in the incident wave packet is found to be &egr;r*/&egr;i*=&ohgr;i*/&ohgr;r* for an oncoming overdense ionization front, for which &ohgr;i*<&ohgr;r* (where &ohgr;i* and &ohgr;r* are the incident and reflected wave frequencies in the laboratory frame). For an oncoming ionization front in the presence of an applied magnetic field normal to the front, &egr;r*/&egr;i* can considerably exceed &ohgr;i*/&ohgr;r*. For a retreating recombination front (&ohgr;i*≳&ohgr;r*), in the overdense unmagnetized case, &egr;r*/&egr;i*=&ohgr;r*/&ohgr;i*. These results have important implications for the production of sub‐millimeter wavelength pulses by upshifted reflection from a relativistically moving ionization front.