  (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-Zel'dovich (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.
