  We explore the potential of several Neutrino Factory (NF) setups to
constrain, discover and measure new physics effects due to Non-Standard
Interactions (NSI) in propagation through Earth matter. We first study the
impact of NSI in the measurement of $\theta_{13}$: we find that these could be
large due to strong correlations of $\theta_{13}$ with NSI parameters in the
golden channel, and the inclusion of a detector at the magic baseline is
crucial in order to reduce them as much as possible. We present, then, the
sensitivity of the considered NF setups to the NSI parameters, paying special
attention to correlations arising between them and the standard oscillation
parameters, when all NSI parameters are introduced at once. Off-diagonal NSI
parameters could be tested down to the level of $10^{-3}$, whereas the diagonal
combinations $(\epsilon_{ee} - \epsilon_{\tau\tau})$ and
$(\epsilon_{\mu\mu}-\epsilon_{\tau\tau})$ can be tested down to $10^{-1}$ and
$10^{-2}$, respectively. The possibilities of observing CP violation in this
context are also explored, by presenting a first scan of the CP discovery
potential of the NF setups to the phases $\phi_{e\mu}, \phi_{e\tau}$ and
$\delta$. We study separately the case where CP violation comes only from
non-standard sources, and the case where it is entangled with the standard
source, $\delta$. In case $\delta$ turns out to be CP conserving, the
interesting possibility of observing CP violation for reasonably small values
of the NSI parameters emerges.
