In "Dax"[DSN1] we have the following exchange when some badguys are trying to abduct a crewmember and escape the station (hat tip: Chakoteya.net):
ODO: They're managing to avoid the security tracking grid. They seem to know a lot about the station.This has generally been used as evidence that the Danube class runabouts have a maximum speed of warp five. Also, early runabout design concepts (wherein they were going to re-use an old TMP-era ship model that later got used as the Sydney Class USS Jenolan in "Relics"[TNG6]) had the runabout limited to warp 4.7.
KIRA: Then they may know the speed of our runabouts. If they do, they probably have a faster ship to make their escape.
SISKO: Major, survey all ships in dock with a high warp capability. Damn!
SISKO: That's why we've got a residual charge in the graviton generator. They've disabled the tractor beam.
KIRA: We've got eight ships in dock capable of warp five or more. Three on docking pylons, five smaller ones in the ports.
SISKO: Seal off all docking ring airlocks.
However, in my opinion, that quote only implies that Kira took Sisko's order about looking for "high warp capability" to mean "warp five or more". Nothing there specifically mentions runabout maximum warp velocity, nor was it ever mentioned throughout the series.
In the context of the episode and the search, this makes sense . . . there's no reason to assume that visiting starships have some sort of advertisement of their actual maximum warp speed. Vessel registrations may include some sort of similar information and that might've been what Kira was looking at, or alternately they may have tried to scan all the ships and take a guess. But either way, the actual truth of the matter was undoubtedly hazy.
Or, put it another way . . . if I wanted to find a ship among several that might be able to outrun the Enterprise-D, I'd search first for any that might be able to exceed warp nine . . . maybe seven or eight if I want to be sure to account for some lead time, trickery, et cetera. That doesn't mean the Enterprise-D is limited to warp eight (as we know), it just means I'm narrowing down the possibilities.
Besides, given that frickin' coffins can accelerate to and maintain warp nine (from "The Emissary"[TNG2]), and given the rather voluminous warp mechanics of the runabout by comparison, and given that runabouts are seen to be capable of evading and escaping from fast ships chasing them ("Vortex"[DNS1], "Apocalypse Rising"[DSN5], "Treachery, Faith, and the Great River"[DSN7], just to name a few) and given that the frickin' Suliban could clock warp five in their little pods 200 years prior, the whole notion of a warp five runabout just doesn't work in context. It would be like the US Navy putting out a PT boat that is propelled at oar-speed.
But unfortunately, people latched on that because there was little else to go on. However, we can ponder another point.
In "The Jem'Hadar"[DSN2], Jake Sisko orders the Rio Grande computer to set a course for DS9 at warp eight. The computer doesn't reject his command on the grounds of velocity correction, but simply notes that the autopilot is not functional. Of course, it might've reacted the same way if he'd ordered warp 13, but the interesting part to ponder is that Jake ordered it at all. You see, a plot point with this episode (and indeed, the early part of the series . . . see "Civil Defense") is that Jake had been assisting Chief O'Brien with assorted maintenance duties, and in this episode we are told that he'd been assisting with runabout maintenance.
Warp eight is a very odd figure to choose if you are desperately asking for a fast speed and unclear on the vessel's maximum velocity. Why not nine, or 9.9 even? Put simply, Jake wouldn't exactly be my go-to guy for tech questions, but he's not completely ignorant, and I think that particular order to the computer is indicative of what he knew of the vessel's velocity capabilities.
Personally, I find this to be fair evidence for warp eight as an attainable velocity for runabouts. It is not absolute proof, but like the Kira search I don't think it is disproof, either.
Of course, we do know from Voyager's "Resolutions" that the Type-9 shuttle (believed to be the speedboat shuttlecraft) has a top speed of warp four, though it is suggested as top speed in the context of a multi-year voyage and thus may represent top cruising speed. One could argue that this should limit the Danube, but again I must point to the voluminous warp mechanics of the Danube versus any of the common shuttles, which are boxes with nacelles . . . where are the reactors? Well hidden and compact!
So, the maximum speed of the Danube Class is unknown, but probably respectably high. She's more a truck than a speedboat, I'd imagine, but I doubt she's a slow truck.
The following was removed on the grounds that popularly available data on the Cardassian ship mentioned is not supported by the canon evidence. See the next post about the Hideki class.
In "Profit and Loss"[DSN2], we have a Cardassian shuttle (a runabout-sized first use of the model that would later be used for the Hideki, then finally as a shuttle again in "Tacking Into the Wind[DSN7]") that is suggested to be capable of warp eight by Quark. Do you really think Cardie ships of that size range are likely to be faster than Federation ones?