Unlike Falkirk, Dunfermline have not yet managed to end their top-flight absence, but will hope this is the season they can end their 14-year hiatus.
They are third in the Championship, out of the running for the title but on course for a play-off spot.
However, they have shown they are more than capable of competing at the top table with their cup performances this term.
Under former Celtic and Hibernian boss Neil Lennon, the Pars have beaten Queen of the South, Hibernian, Kelty Hearts and holders Aberdeen.
Despite those wins over top-flight teams, the former Northern Ireland midfielder expects a stern test against McGlynn, describing him as "one of the best coaches" in Scottish football.
Lennon also believes his opposite number on Saturday could be the man to take Celtic forward when interim boss Martin O'Neill departs in the summer.
"He's learned, he's worked hard and he's reaping the rewards of it," he said. "He's a sponge and I know he's very thorough in his detailed approach."
Lennon is a serial winner in this competition - four times he lifted the trophy as a player and four more as a manager.
Doing so with Dunfermline would be one of his finest achievements in management and, despite his long career in the dugout, Lennon is as hungry as ever for success.
"I have this real inner drive to succeed and keep going," he said.
"I don't think I have anything to prove to people, I don't really bother about that. It's proving to myself what I can achieve and what more I can do.
"This is the next step for me, trying to get to a cup final and into the Premiership."
To achieve the first of those goals, Lennon will have to find a way to stop one of the most talked-about young players in Scottish football - a man he knows well.
Barney Stewart has played a key role in Falkirk's success this season, scoring 10 goals in 17 appearances.
That is off the back of a prolific loan spell at Dunfermline in the first half of this campaign, during which he netted eight in 12.
"Barney's gone on to do really good things this season," Lennon said. "In the box, he's dynamite. A lot of his goals are one-touch finishes.
"He scored eight goals in 12 games here. The challenge was, could he take it on into the Premiership? He's done that.
"I think he surprised a lot of people. He's had a meteoric six months. Credit to him. He's a good lad as well."

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