  Quasiparticle poisoning and diabatic transitions may significantly narrow the
window for the experimental observation of the $4\pi$-periodic $dc$ Josephson
effect predicted for topological Josephson junctions. Here, we show that
switching current measurements provide accessible and robust signatures for
topological superconductivity which persist in the presence of quasiparticle
poisoning processes. Such measurements provide access to the phase-dependent
subgap spectrum and Josephson currents of the topological junction when
incorporating it into an asymmetric SQUID together with a conventional
Josephson junction with large critical current. We also argue that pump-probe
experiments with multiple current pulses can be used to measure the
quasiparticle poisoning rates of the topological junction. The proposed
signatures are particularly robust, even in the presence of Zeeman fields and
spin-orbit coupling, when focusing on short Josephson junctions. Finally, we
also consider microwave excitations of short topological Josephson junctions
which may complement switching current measurements.
