The Vestal Aemilia's prayer
VestaDionysius of Halicarnassus tells how the sacred fire went out during the watch of the Vestal Aemilia. By Roman reckoning this was itself the evidence: the fire goes out when the priestess is impure. She was accused — and these are her words at the altar.
The prayer is built as a self-curse turned into proof. "If I have performed the rites for you in a holy and righteous manner … appear to me and help me; but if I have done anything impious, let my punishment purge the pollution of the city." With its second half she offers herself up.
That is the point. Roman religion had no way of proving innocence by argument: the accused handed herself to the god and waited for the outcome to speak. According to Dionysius, Aemilia threw a strip of her linen garment onto the cold altar, and the flame blazed up.
One caveat: Dionysius writes in Greek about a Roman rite and calls Vesta by her Greek name, Hestia. He does not date the episode himself.