There are only four actual E-D saucer separation events in TNG: "Farpoint", "Arsenal of Freedom", "Best of Both Worlds" and ST:Generations. In addition, separation is considered but dismissed in "Heart of Glory" as a precaution before entering a potential battlefield, and in "Brothers" as a means of depriving Data of the control of the ship. An explosion separates the saucer of the Yamato in "Contagion", and supposedly also that of the Odyssey in "Jem'Hadar" although the VFX is less clear there.
Yet it's only in "Farpoint" and "Arsenal" that the saucer is supposed to engage in travel on its own. In "Farpoint", we witness it flying across a distance that the combined ship covered at extreme warp during several minutes of flight at least - so we know the saucer can maintain at least medium warp after high-warp separation. In "Arsenal", though, the saucer is jettisoned at impulse, yet supposed to travel to a distant starbase in another star system. If giving a warp boost with the stardrive section was necessary or even helpful in saucer warp travel, surely it would have been done in "Arsenal" - so this is another bit of indirect proof that the saucer can accelerate to warp on its own.
Neither of these eps establishes the warp speed of the saucer, though. In "Brothers", it is discussed that the saucer will drop out of warp two minutes after separation - but this need not always be the case. The whole point of the separation here is to sabotage the ship so that Data can't make use of it, so it would also make sense to perform the separation in such an exceptional manner that it sabotages the saucer's ability to maintain or reach warp. Probably not difficult to do when the saucer lacks all crew except for Data, and when our heroes clearly do their best to sabotage the computers and automated systems of the saucer while Data fights back.
Apart from all of that, warp 3 sounds plausible for a massive saucer-shaped starship with internally mounted and thus probably relatively weak engines. And internal warp engines certainly aren't unheard of in Federation starships (say, the Defiant), let alone alien ones.
Timo Saloniemi