Edinburgh's third club - who joined the Scottish League 20 years ago - are set to leave the capital for nearby Livingston next season, changing their name to that of their new home town in the process. So if Saturday's fourth-round tie follows form, it will be the last time the name Meadowbank appears in the Scottish Cup records.
Apart from the newcomers Caledonian Thistle, Celtic are the only team that Meadowbank have never faced since coming into the League (they have met Ross County in the Scottish Cup). Celtic's is the only ground they have not visited and, even though Saturday's tie takes place at the Glasgow giants' temporary base, the Meadowbank party will have the chance to view Parkhead, which is under reconstruction.
That is because Celtic have invited the part-timers to have their pre-match meal at the stadium before they head for Hampden and the Cup-tie.
"It's a great gesture for a club like Celtic to come forward and offer us their facilities," the Meadowbank midfielder Dougie Samuel said. "Some of us still can't believe we're playing against them at Hampden for a place in the last 16 of the Scottish Cup.
"I've heard these matches are over all too quickly and I just want to relax and enjoy the day. I'm just hoping I'm one of the lucky players who is given one of the 14 shirts on the day."
When Meadowbank, previously known as Ferranti Thistle, joined the Scottish League in 1975, their supporters were so few they used to travel on the team bus to away matches. They expect to take around 500 fans to Hampden and are expecting a £60,000 pay-out.
It will be a particularly poignant occasion for the 83-year-old honorary president and former chairman, John Blacklaw, who has been involved with the club since their early days. Perhaps optimistically, Meadowbank have booked Hibernian's nearby Easter Road ground for the replay.
Jimmy Nicholl, Raith Rovers' manager, is fighting desperately to hold on to the young players who have given the club unprecedented success this season.
Nicholl has enjoyed astonishing fortunes in his time at Kirkcaldy, culminating in the Coca-Cola Cup final victory over Celtic in November. With several of Scotland's brightest youngsters in his squad, it is little surprise that scouts have been beating a path to Stark's Park where Steve Crawford, Jason Dair and Colin Cameron have all attracted attention.
"If I can I will hold on to them, but there have been offers for some of my players," Nicholl, the former Northern Ireland international full- back admitted. "I am actually refusing money for them just now because I want to get into the Premier Division and into Europe next season with my best players. I am fighting tooth and nail to keep them.
"However, I know that only if we reach the next stage in the club's progress will I be able to keep on holding on to players. On our gates, we can't afford to keep lads who could have a future elsewhere and we won't be able to until we become a well established provincial club with gates of 8,500 to 9,000. I can't complain about the 4,000 or so regulars who come to watch us, but we still have some way to go."
Nicholl will once again give the nod to his young players for Saturday's Tennents Scottish Cup fourth-round tie against Dundee at Dens Park. However, Dundee's losing streak coupled with his own side's good run has made Nicholl a surprisingly worried man.
He admitted: "We have won our last nine games while Dundee have lost their last three - and something tells me that something has to give at some point. We have got to lose some time and Jim Duffy will be telling his players that their run has to come to an end.
"I certainly don't believe in the manager's line that a cup defeat means they will concentrate on the League. I want to win the League more than the Cup, but a Cup run can keep the players super-confident and there's the thrill of being in the draw - that's something I don't want to miss out on. Success breeds success. Perhaps we didn't have an inner confidence before, but we do now having won the Coca-Cola Cup."