  Radio relics are patches of diffuse synchrotron radio emission that trace
shock waves. Relics are thought to form when intra-cluster medium electrons are
accelerated by cluster merger induced shock waves through the diffusive shock
acceleration mechanism. In this paper, we present observations spanning 150 MHz
to 30 GHz of the `Sausage' and `Toothbrush' relics from the Giant Metrewave and
Westerbork telescopes, the Karl G. Jansky Very Large Array, the Effelsberg
telescope, the Arcminute Microkelvin Imager and Combined Array for Research in
Millimeter-wave Astronomy. We detect both relics at 30 GHz, where the previous
highest frequency detection was at 16 GHz. The integrated radio spectra of both
sources clearly steepen above 2 GHz, at the >6$\sigma$ significance level,
supports the spectral steepening previously found in the `Sausage' and the
Abell 2256 relic. Our results challenge the widely adopted simple formation
mechanism of radio relics and suggest more complicated models have to be
developed that, for example, involve re-acceleration of aged seed electrons.
