Depends on how you define formal, in diplomatic settings and academic/scientific discussions it was common until French became popular during the Enlightenment

When Athanasius Kircher met with Nicholas Calude Fabri de Peirsec in the 1630s they probably spoken to each other in Latin.
Source: John Glassie A Man of Misconceptions:The Life of an Eccentric in an age of Change

Also the Irish Pirate Queen Grace O'Malley is believed to have conversed with Queen Elizabeth I in Latin when they met in 1593