The Romans mostly seem to have made up the battle speeches (and the readers knew they were fake and read them for entertainment). Do we have any actual recorded battle speeches? Is it much different from Hollywood?
So I don't know about actual verbatim reports of battle speeches, but I want to clear up a misconception you have about Roman speeches.
The notion that the speeches we have in ancient history are fake is... exceptionally skeptical if not flat out wrong. This whole line of thought derives from Thucydides, who said speeches were hard to remember, so he supplies the best he can, and what must have been said for the situation.
That's usually taken by people encountering it for the first time (and indeed by a number of scholars as well) as Thucydides made up his speeches. But note that Thucydides doesn't say he's making up the fact that speeches were given (if he's making them up at all - he said he does that when memory fails). Speeches before battle WERE given. Boudicca, we're told, lost that last battle because some of her soldiers didn't hear the speech and charged at an inopportune time. That only makes sense if there was an actual speech, and it's not just a feature of Roman entertainment.
There's a very famous speech Claudius gave to the senate in 48 CE on the admission of the Gauls to the senate. Tacitus gives us one version; we happen to have what seems to be a verbatim account in an inscription in Lyons. They are not the same. Tacitus clearly knew the contents of the speech, judging from the inscription. He hits similar points, he counters similar objections. What he did for the "entertainment" aspect was rewrite it so the logic is tighter, the language is neater. He didn't think he could just make a speech up; he felt some need to conform to the sense of the delivered speech, but he dressed it up to make it look pretty.
You shouldn't be thinking about these speeches made up for fun, for the most part. They're fitted to a particular literary purpose, but they aren't completely imaginary.
EDIT: If you will accept a verbatim report of a political speech, this speech by Claudius in 48 CE might qualify.
I have no idea, thus the question, but my probably innacurate presumption would be it was mostly like Stannis before the Battle of Blackwater: "Come with me and take this city!", rather than something like Aragorn's speech or Theoden's speech in the third Lord of the Rings film.