Based on a recent proposal to build an electron-muon collider, we study two-to-two production processes $e^{-}{\mu }^{+}⟶f\overline{f}$, $\gamma \gamma$ that originate from dimension 6 and 8 operators. We compare the sensitivity to those effective couplings obtained at the collider with that of low energy measurements of $\mu ⟶e\gamma$, $\mu ⟶e\overline{e}e$, and $\mu ⟶e$ conversion that have recently been reported in the literature. Whereas for the production of first family fermions, the sensitivity of the collider processes is much weaker; for the second and third family fermions, it is similar or stronger than that of low-energy processes. In the case of $e^{-}{\mu }^{+}⟶\gamma \gamma$, the sensitivity to a dimension 8 contact operator turns out to be the strongest in comparison.