Both sides head into the clash at Tynecastle level on points and seeking to close the gap on front-runners Motherwell, Hibernian and Celtic.
However, in the absence of Rangers in the SPL this season, Shiels believes expectations are high for Hearts to show they can be the second force in Scottish football.
He said: “It’s the first time we’ve come up against them now that they’re the second biggest club after Celtic.
“They’ve got a lot of pressure to finish in second place.
“They were the last club to split the Old Firm and I feel there’s pressure on Hearts to finish second now. With the armoury and players that they have and the infrastructure and the salaries and the wages - that brings its own pressure.”
Saturday’s game will be the first time Shiels has gone up against Hearts counterpart John McGlynn and the Kilmarnock manager has been impressed by his opposite number so far.
He said: “He’s given the young boys a chance and, in terms of promoting young players and giving them opportunities, he’s right up there. He’s done a great job in that department. He’s a good guy. I’ve met him at a couple of things and he’s a good person.
“He’s a good football man. He’s steeped in the tradition of being in the game and working to improve and develop young players, a similar role to what I’ve done in the past as well.
“I see him as a great ambassador for bringing in young players and trying to promote the game in Scotland.”
McGlynn’s predecessor Paolo Sergio had a well-publicised falling-out with Shiels, once threatening to “shake his neck”. But the current Tynecastle manager was a bit more complimentary about his opposite number.
“This will be my first time up against Kenny,” McGlynn said.
“He’s good for the media: he’s opinionated.
“Everyone’s different. Guys like me are boring – Kenny’s great value for you guys.”