  We find the admittance of a topological Josephson junction
$Y(\omega,\varphi_0, T)$ as a function of frequency $\omega$, the static phase
bias $\varphi_0$ applied to the superconducting leads, and temperature $T$. The
dissipative part of $Y$ allows for spectroscopy of the sub-gap states in the
junction. The resonant frequencies $\omega_{\mathcal{M}, n} (\varphi_0)$ for
transitions involving the Majorana ($\mathcal{M}$) doublet exhibit
characteristic kinks in the $\varphi_0$-dependence at $\varphi_0=\pi$. The
kinks -- associated with decoupled Majorana states -- remain sharp and the
corresponding spectroscopic lines are bright at any temperature, as long as the
leads are superconducting. The developed theory may help extracting
quantitative information about Majorana states from microwave spectroscopy.
