We study the stability of periodic trajectories of planar inverse magnetic billiards, a dynamical system whose trajectories are straight lines inside a connected planar domain $\Omega$ and (magnetic) Larmor arcs outside $\Omega$. Explicit examples are calculated in circles, ellipses, and the one parameter family of curves $x^{2k}+y^{2k}=1$. Comparisons are made to the linear stability of periodic billiard and magnetic billiard trajectories.