  An important experimental signature of localization is the low-frequency AC
conductivity, which typically vanishes as $\omega^{\phi}$. The exponent $\phi =
2$ for Anderson insulators, whereas for many body localized insulators $\phi$
is a continuously varying exponent $1 \le \phi \le 2$. In this work, we study
the low-frequency AC conductivity of localized superconductors, in which
disorder is strong enough to localize all quasiparticles, while remaining weak
enough to leave superconductivity intact. We find that while the ac
conductivity still follows the general form $\sigma(\omega) \sim
\omega^{\phi}$, the exponent $\phi$ can be markedly different from the
characteristic value for localized insulators. In particular, in certain
symmetry classes at zero temperature, we obtain $\phi > 2$. We further identify
an interesting temperature dependent crossover in the scaling form of the AC
conductivity, which could be useful for the experimental characterization of
localized superconductors.
