Characterising the structural dynamics of proteins and the effects of excipients are critical for optimising the design of formulations. In this work we investigated four lyophilised formulations containing bovine serum albumin (BSA) and three formulations containing a monoclonal antibody (mAb, here mAb1), and explored the role of the excipients polysorbate 80, sucrose, trehalose, and arginine on stabilising proteins. By performing temperature variable terahertz time-domain spectroscopy (THz-TDS) experiments it is possible to study the vibrational dynamics of these formulations. The THz-TDS measurements reveal two distinct glass transition processes in all tested formulations. The lower temperature transition, Tg,$β$, is associated with the onset of local motion due to the secondary relaxation whilst the higher temperature transition, Tg,$α$, marks the onset of the $α$-relaxation. For some of the formulations, containing globular BSA as well as mAb1, the absorption at terahertz frequencies does not increase further at temperatures above Tg,$α$. Such behaviour is in contrast to our previous observations for small organic molecules as well as linear polymers where absorption is always observed to steadily increase with temperature due to the stronger absorption of terahertz radiation by more mobile dipoles. The absence of such further increase in absorption with higher temperatures therefore suggests a localised confinement of the protein/excipient matrix at high temperatures that hinders any further increase in mobility. We found that subtle changes in excipient composition had an effect on the transition temperatures Tg,$α$ and Tg,$β$ as well as the vibrational confinement in the solid state. Further work is required to establish the potential significance of the vibrational confinement in the solid state on formulation stability and chemical degradation as well as what role the excipients play in achieving such confinement.