The influence of low to moderate frequency environments on Macroscopic Quantum Tunneling (MQT) in superconducting circuits is studied within the Im-F approach to evaluate tunneling rates. Particular attention is paid to two model environments, namely, a pure sluggish bath and a sluggish bath with additional 1/f-noise. General findings are applied to Zener flip tunneling, a MQT phenomenon recently predicted and observed in a superconducting circuit implementing a quantum bit.
