A trophy that has evaded them thus far, the Perth outfit weathered an early Hibernian onslaught to defeat the Leith side 3-0 at Hampden on Saturday and give themselves a shot at making history.
And the occasion brought back some very happy memories for Conway while furnishing him with many more.
“I don’t mind Hampden, to be honest,” said the 35-year-old midfielder, who would love to add another medal to the Scottish Cup bauble he won with Dundee United in 2010.
“I’ve had some great times here, especially in that cup final and today, but also the semi-final in the Scottish Cup, the year we won it. I just love playing here.
“It would be so much better if there were fans, but there’s just something about the place. I get a good feeling here. I have got a lot of happy memories here and hopefully we can take this one step further and give me another day to talk about.”
They will return to Glasgow on February 28 when they will face Livingston in this season’s Betfred Cup final.
And Conway knows how special those days are having delivered a man of the match performance the day the Tannadice side lifted the silverware.
“Yeah, 100 per cent. I’ve had other big days in my career, I’ve been lucky enough to gain promotions and stuff like that but that day in particular [when Dundee United won], the whole atmosphere, you could see what it meant to the city.
“It’s hard because you are not seeing the fans every week at McDiarmid. They are not getting in to watch us. But I’m sure there will have been a lot of happy faces watching us on TV. We have games before the final, but there’s no doubt about it, the final is a massive chance for us to go and win something.
“I must admit, I probably didn’t think that chance would come again. But we just ticked the rounds off and we found ourselves in a semi-final. We knew it was a big chance for us and, luckily enough, we got through. I felt we were pretty convincing.”
That wasn’t the case early in the game when they had trouble getting out of their own half as Hibs piled on the pressure but, showing they had patience, resolve and belief, Saints bided their time and then hit their rivals where it hurt.
Having established the lead when Jason Kerr rose above the Hibs defence to convert David Wotherspoon’s 35th minute corner, Craig Conway killed off the Easter Road side’s hopes of a comeback, firstly flighting in a free-kick for Shaun Rooney to attack and head past Ofir Marciano. Rooney then turned supplier and it was Conway darting in at the back post to wrap things up.
“We’ve got winners in this squad and we know that it’s one thing getting to a final – now it’s about winning it.”