Thermodynamic measurements of magnetic fluxes and I-V characteristics in
SQUIDs offer promising paths to the characterization of topological
superconducting phases. We consider the problem of macroscopic quantum
tunneling in an rf-SQUID in a topological superconducting phase. We show that
the topological order shifts the tunneling rates and quantum levels, both in
the parity conserving and fluctuating cases. The latter case is argued to
actually enhance the signatures in the slowly fluctuating limit, which is
expected to take place in the quantum regime of the circuit. In view of recent
advances, we also discuss how our results affect a π-junction loop.Comment: 10 pages, 11 figure