  We analyze the New Physics sensitivity of a recently proposed method to
measure the CP-violating ${\cal B}(K_S\to\mu^+\mu^-)_{\ell=0}$ decay rate using
$K_S - K_L$ interference. We present our findings both in a model-independent
EFT approach as well as within several simple NP scenarios. We discuss the
relation with associated observables, most notably ${\cal
B}(K_L\to\pi^0\nu\bar\nu)$. We find that simple NP models can significantly
enhance ${\cal B}(K_S\to\mu^+\mu^-)_{\ell=0}$, making this mode a very
promising probe of physics beyond the standard model in the kaon sector.
