The context in which they are doing so this weekend has been well documented as negotiators battle over the future of Scottish teams in Europe's top competition against a background of unprecedented failure on the international front.
On the face of it, Glasgow look to have the better chance of producing the result that would prevent another Scottish "whitewash", this time a first in the history of European competition.
Edinburgh, after all, are heading south to meet a formidable Saracens side who thrashed them at Murrayfield. Furthermore, it is a measure of where things are in the capital that a performance in which they rallied late on to reduce last week's defeat to a nine-point margin, was deemed sufficient improvement to draw what is pretty much a vote of confidence from their management.
By contrast, Glasgow's performance in the away match at Northampton, in which the coach Gregor Townsend believes they played their best attacking rugby of the season for the first 35 minutes, ought to offer considerable hope they can finish with a flourish at home.
Yet, where Michael Bradley has made just one change to his Edinburgh side for the trip to Watford, Townsend's selection for today's match looks to owe at least as much to managing his squad with international and forthcoming RaboDirect Pro12 demands in mind as it does to being competitive in its own right.
A dozen changes, two positional and 10 personnel, would otherwise be considered extraordinary and he admitted, for example, that Rob Harley, who has done some exceptional work in recent works, probably could have played had this been a more significant encounter.
Since his team's Pro12 bid – they sit second in the table – provides the last chance of redemption for the Scottish teams in a season when so much was expected as resources were pumped into them, Townsend probably needs to be a bit cautious. Warriors have 19 of his players in the Scotland squad announced this week, and three more invited to join the camp while injured. Others, such as Tom Ryder and Graeme Morrison, are on the fringes while Rory Lamont has suffered a setback with inflammation flaring in the ankle that kept him out for the past year. All of which means Glasgow's strength in depth will be examined thoroughly as they try to maintain their challenge for a play-off place.
However, such has been the bolstering of resources this season that they ought to be able to cope and Townsend believes that, for all the changes he has made, the quality of players he has been fielding should have done much better in this tournament. "It's been frustrating . . . disappointing," he said.
"We don't want to finish the Heineken Cup season with no wins. We know we've been competitive and we've led in a few of the games. Northampton away and Castres away spring to mind, but we've got to transfer the work we've done in those games to produce a winning performance."
He admitted that, in Northampton, in the opening match in particular, the issue was more mental than physical.
"I thought we could have kicked and kept on playing till half-time," he said, after making that observation about the quality of their play in those opening 35 minutes.
"There was an element of belief involved. We were 15-nil up against the leading team in England . . . should we sit back or could we have really hammered home our momentum? There were some unfortunate circumstances. Stuart [Hogg] picked up an injury and two others picked up injuries in the back line as well which disrupted our rhythm, but it's more where we were as a team, I believe, that we didn't keep on playing."
Perversely, where one of the problems that day was that a calculated gamble on listing only two replacement backs backfired as they were forced into major reshuffles by those injuries, this time Glasgow's on-going injury crisis among front and back-row forwards means they have listed four backs on the bench this time.
That involves Alex Dunbar, one of those newly called into the Scotland squad as a centre, covering the back-row and while that may raise some technical issues in the set-piece it only emphasises just how much pace they should be able to maintain if they can start testing the mobility of Northampton's bulkier men once more.
Indeed, it is quite a state of affairs when the aforementioned Hogg, who did so much to inject hope for the future amid all the gloom last year, is speaking about struggling to keep up with a team-mate, but that is what he was doing yesterday.
"It's pretty frustrating when you do your speed tests and you're going flat out and Sean Maitland is just coasting along, cruising by," the 20-year-old said, grinning cheerfully.
"The problem is he's not got as fat an arse as me to drag along. What he has got is bags of ability and I'm looking forward to seeing him this weekend and in the international squad as well."