(Abridged) Radio relics in galaxy clusters are believed to be associated with powerful shock fronts that originate during cluster mergers, and are a testbed for the acceleration of relativistic particles in the intracluster medium. Recently, radio relic observations have pushed into the cm-wavelength domain (1-30 GHz) where a break from the standard synchrotron power-law spectrum has been found, most noticeably in the famous Sausage relic. In this paper, we point to an important effect that has been ignored or considered insignificant while interpreting these new high-frequency radio data, namely the contamination due to the Sunyaev-Zeldovich (SZ) effect that changes the observed synchrotron flux. Even though the radio relics reside in the cluster outskirts, the shock-driven pressure boost increases the SZ signal locally by roughly an order of magnitude. The resulting flux contamination for some well-known relics are non-negligible already at 10 GHz, and at 30 GHz the observed synchrotron fluxes can be diminished by a factor of several from their true values. Interferometric observations are not immune to this contamination, since the change in the SZ signal occurs roughly at the same length scale as the synchrotron emission, although there the flux loss is less severe than single-dish observations. We present a simple analytical approximation for the synchrotron-to-SZ flux ratio, based on a theoretical radio relic model that connects the non-thermal emission to the thermal gas properties, and show that by measuring this ratio one can potentially estimate the relic magnetic fields or the particle acceleration efficiency.
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