Yeah, The Captains' Honor
by David and Daniel Dvorkin. Its interpretation of the so-called "Magna Roma" was rather off-base. "Bread and Circuses" showed a planet with alien continents (the same shape as half the other planets in TOS) but a similar ratio of land to ocean, atmospheric composition, gravity, climate, etc. to Earth -- like Earth, but clearly not Earth. Yet TCH interpreted it as an absolutely exact duplicate of Earth right down to every individual and historical event, diverging only with Sejanus's attempted assassination of Tiberius. (Which was an in-joke, because Patrick Stewart played Sejanus in I, Claudius
. So having the modern captain be a namesake and near-lookalike for Sejanus was meant to suggest Patrick Stewart vs. himself.)
The idea of the Roman planet being a Federation member just a century after B&C is difficult to believe. They would've had to banish slavery, abandon war, achieve warp drive, etc. in just a hundred years -- that doesn't seem probable.