Roman wars were, according to Livy, supposed to be started by a special ceremony called the "fetial rite," in which a specially designated priest would hurl a ceremonial spear across the border into the enemy's territory. Octavian mimicked this when starting his own war against Antony, but otherwise the fetial law was honored in the breach. There's a discussion of it in this thread on Roman just war theory.

Livy, in The War with Hannibal, relates that a Roman embassy was sent to Carthage to demand the withdrawal of Carthaginian troops from disputed parts of Spain. The Roman ambassador held the folds of his toga in both hands and claimed that in one hand he held war and in the other, peace. Upon the Carthaginian reply that they did no care and for him to choose, the Roman ambassador dropped the folds and stated 'we give you war!'

Much much later, a Roman embassy was sent to demand that the Seleucid Empire withdraw from Egypt.

So it would appear that a diplomatic delegation with an ultimatum, backed up by the power to declare war was common.