Contesting their fifth quarter final in six seasons, Robbie Neilson is hoping his Hearts team can convert that into their fourth final in the same period, and, ultimately, their first win since 2012. After holding their own for an hour of the midweek league meeting which ended 3-1 to Celitc, building on the 4-3 loss the last time the pair met at Tynecastle, the Gorgie side know they have the capacity to match Ange Postecoglou’s men for periods of a match and Neilson accepts that if they are to smash through the glass ceiling that separates the rest of Scottish football from the two Glasgow sides who are operating at a level above, then Saturday afternoon’s match represents as good a platform as any.

“For the last 20 or 30 years one of Celtic or Rangers have been the dominant force so you’re having to play these teams maybe six times a season [including cup competitions],” said Neilson. “We know [Celtic] are a top, top team, there’s no doubt about that, and we will have to be at our best to break that run. But that’s the objective for us, that’s what we want to do. If we are going to have any chance of doing it then this is probably the day. We’re at our peak at the moment, we’re playing at home, it’s a cup game, it’s all or nothing, so we’ll see what we can do.”

The all or nothing aspect of the game means that Neilson could be more likely to take chances on the men who have proved that they can take chances, with Lawrence Shankland, who opened the scoring against Hibs in the previous round, and Josh Ginnelly, who also contributed that day and then scored against Celtic in the league on Wednesday, both being given until the last minute to declare themselves fit. But the fact that it will be contested at Tynecastle, where Hearts previously ended Celtic’s invincibles’ run, and more recently put three goals past them, albeit then conceding four, offers hope.

Stephen Kingsley will be part of a Hearts defence looking to spring a surprise on Celtic.

“When you are scoring three goals against Celtic you would be hoping that would be enough,” admitted defender Stephen Kingsley. “But to concede four goes back to that thing of competing with them, getting close, and that final step being missing. That is what has been disappointing but it does give us confidence and we are looking forward to the game. If you take the positives from previous meetings, we know we can do it when we are on it. We just need to see games out and be a bit more resilient.

“We have said it all along that if you are going to have aspirations of winning the cup then you will probably have to play one of the top two at some point. So, to have them at Tynecastle, which will be bouncing, with that carrot of knowing that if you win you get to Hampden, is brilliant. And, it has been proven that when we play well and we’re on it, we can match them. I think the atmosphere will be a massive positive for us.”

A chance to advance the dream of lifting silverware, it is also an opportunity for Neilson’s men to get one step closer to a European entry point which would grant them UEFA group stage football again next season. All of that matters to Kingsley. But, he is honest enough to concede that it could also be a way of helping to exorcise ghosts. It was early in his Hearts career when he was parachuted into the postponed conclusion of the 2019/2020 Scottish Cup and the conclusion is not one he will forget, as he fluffed his lines in the penalty shootout.

“It was in the season where we actually played the previous season's Scottish Cup final,” recalled Kingsley. “I'd just arrived and then a couple of weeks later we're playing Hibs in the closed-door semi-final at Hampden then going into the final. In the final I thought we were disappointing in the first half but did very, very well in the second half to get back into it. We played well to fight back into the game and it was just a match where we gave everything.

Hearts took the lead via Josh Ginnelly during the midweek match against Celtic.

“To lose it on penalties, it's always going to be disappointing to look back on. But outwith that we can look back and know we gave absolutely everything we had. When it gets to that stage, tiredness can kick in and it's unfortunate how it ended. It is something you’re going to carry for the rest of your life in terms of what might have been. But if you get hung up on every disappointment in football then no-one would have a career because there will be low points in every career.”

The head and the heart will always be at odds when looking back on such pivotal moments but realism should never be mistaken for acceptance of glorious failure. Hearts’ ambition soars higher than that, according to the former Scotland left-back. “No, we don’t want that idea of heroic failure,” added Kingsley. “We have to take the positives from the other night but we know we need to do better in terms of the goals we conceded. I can’t remember seeing too many teams who have gone to Parkhead and played the way we did, especially in the first half and for little periods in the second. So, that is a great confidence booster, knowing that when we’re on it, we have the players and the quality to go to places like that and show glimpses of what we can do. We just need to do it over 90 minutes.”

Smashing the Celtic-Rangers glass ceiling: Hearts know it is time to make a move on Old Firm