Today they stand a possible 12 games away from a potential return to English football’s top flight.
The 17 years in between has been a remarkable roller-coaster ride at Hillsborough, including three relegations and two promotions.
Palmer has been witness to it all, having first joined the Owls as a seven-year-old in 1997.
Now 24 and with over 100 games under his belt, the Worksop-born defender has been a key squad player under Carlos Carvalhal this term.
He has alternated with Jack Hunt for the right-back shirt this season, but in his last three outings Palmer has been part of a Wednesday defence which has kept clean sheets on their travels at Hull City, Brighton and Nottingham Forest.
It has left the Owls in the Championship’s top six, with nine games of the regular season remaining, and possibly the play-offs to come.
“Getting promoted would be a massive achievement,” said Palmer.
“All the players must have it in the back of their mind.
“We have been slowly progressing throughout the season, we have that sixth spot, and we want to maintain that.
“Being here, coming through the gates for 17 years, it’s difficult to put into words what promotion would mean to me.
“We got promotion once, how good would it be to get a second one, what an achievement.”
Palmer was part of the League One promotion-winning side, a regular under Gary Megson, before Dave Jones took over.
He is one of the main success stories to come out of the Owls Academy over the last decade.
“I first joined when I was seven, they had an under-8s programme, and my first full season was the under-9s.
“The gates haven’t changed, but a lot of things inside have in a positive way, this season particularly.
“I have seen the ups and downs, a lot of personnel have changed with the players and staff.
“But one thing that has never changed is the fans.
“Look at Tuesday night at Brighton and the numbers we had down there. If Forest had given us the bottom tier, we would have filled it.
“With the exciting players we have now, the fans are coming in their numbers and we just want to repay them.
“The bubble of excitement is going to draw the crowds in, there is an expectation we have put on ourselves.”
A crowd of 30,000 is expected at Hillsborough today for the visit of Charlton Athletic, with the Leppings Lane stand lower tier even open for home supporters, such is the demand for tickets.
The visitors are fighting for their lives at the bottom of the Championship, but one of their rare wins this season came against Wednesday in a 3-1 victory at The Valley.
The Owls have also lost to fellow strugglers Milton Keynes Dons and Rotherham United – 1-0 in their last Hillsborough outing – so know they cannot take Charlton lightly.
Palmer said: “They showed down at their place what a good side they can be on the day and fully deserved the three points.
“It’s a tight league, and Charlton are coming off a good win against Middlesbrough. Nobody saw that coming before the game. Anyone can beat anyone on their day in the Championship.
“We have a good record at home, we need to show Rotherham was a blip, and bounce straight back.
“A factor this season has been when we have had disappointing results, we have bounce dback, played with a bit of anger and disappointment that we have let ourselves down.
“Even when we are not playing at our best, we have players who can make things happen, out of the blue, that’s what’s exciting about this team.”
The rotation policy Carvalhal employs could cause problems in some dressing rooms, but Palmer – himself a victim of the chopping and changing – believes a winning formula has helped soothe any apprehensions players may have had.
“I have enjoyed it this season, it’s been an exciting season, even just watching the brand of football we have been playing,” said Palmer.
“Obviously, you do get frustrated because you want to play every game. But whether it’s me or Jack (Hunt), or on the left Dan (Pudil) or Joe (Bennett), we all know what we need to do when call upon.
“We have all shown we are capable of putting in good performances.
“Going out on loan never crossed my mind. When you are not playing, you’re working hard on and off the pitch. Every time I have had a chance, I have just done my best and shown the manager he can trust in me when he sees fit.
“Rotation has shown over a period of time that it has worked. When he has freshened things up, it’s not just one game where we have got a result, but the game after that when it’s allowed players to return with freshness and energy.
“When you see that working, it’s a lot easier to buy into than if you are down the bottom and the team keeps getting changed a lot.”
The Owls will be forced into one change from the side which swept aside Forest with ease last weekend, with Barry Bannan starting a three-game ban for his red card at the City Ground.
Lewis McGugan, Sam Hutchinson and Alex Lopez look the likely replacement options for Carvalhal to ponder.
“Baz will be a big loss, he’s one of our main components to get us playing, said Palmer.
“We have got players ready to step in, though, and fill his boots.”