$THH$ and base-change for Galois extensions of ring spectra

We treat the question of base-change in $THH$ for faithful Galois extensions of ring spectra in the sense of Rognes. Given a faithful Galois extension $A \to B$ of ring spectra, we consider whether the map $THH(A) \otimes_A B \to THH(B)$ is an equivalence. We reprove and extend positive results of Weibel-Geller and McCarthy-Minasian and offer new examples of Galois extensions for which base-change holds. We also provide a counterexample where base-change fails.