Caligula's Caligae are a pair of leather sandals worn by Caligula to navigate the Labyrinth to get to Herophile's prison. These sandals gave Caligula his childhood nickname.
The Trials of Apollo

Caligula, the owner
The Dark Prophecy
The Caligae are mentioned in the sonnet prophecy “To walk the path in thine enemy’s boots."
The Burning Maze
After breaking in to Caligula's yachts and stealing the sandals, Apollo wears them to guide him, Meg McCaffrey and Grover Underwood to Herophile's prison within the Labyrinth. After they save the Oracle and return to Aeithales, Apollo discards the sandals.