We consider the impact of non-standard interactions of neutrinos (NSI) on the determination of neutrino mixing parameters at a neutrino factory using \(\pnu{e}\to\pnu{\mu}\) ``golden channels'' for the measurement of \(\theta_{13}\). We show how a small residual NSI leads to a drastic loss in sensitivity in \(\theta_{13}\), of up to two orders of magnitude. This can be somewhat overcome if two baselines are combined.