The clubs have previously met twice in the League Cup in its various guises, with Rotherham handing the Merseysiders a scare en route to elimination under the old two-legged format.
A second round encounter in 1992-93 saw the Millers triumph 1-0 at Millmoor before losing the return leg 3-0 and, five seasons earlier, the South Yorkshire outfit went even closer to recording a major upset.
After losing 3-2 in the away leg, the Millers drew 0-0 on home soil and were narrowly edged out on aggregate in another second-round tie with the Toffees, who were then reigning Division One champions.
Around 2,000 Millers fans will travel across the M62 in the hope of witnessing more cup drama tonight against Everton, whose last major trophy arrived in 1995 – with the club now managed by former Hull City chief Marco Silva.
Warne, likely to utilise his squad this evening and field a line-up similar to the one who beat Wigan Athletic 3-1 in the previous round, said: “I expect them to play with a real energy and a vigour and they will want a cup run this year. They will cause us a really difficult evening. But I expect my lads to do the same.
“I just want the lads to enjoy playing at Everton; they might not ever play there again. I want them to enjoy the atmosphere and tradition. It just smells of football there. If we perform to a level and have a right go, that is all we can ask.
“Both of us want to go through, but will see the bigger picture. Will he (Silva) risk his bigger stars against us? Possibly not and I understand why.
“In fairness, I think they have got the best under-23s team around and if he was to dip into any of his younger pros, they are excellent.
“You only have to look at Joe Williams, who went to Barnsley last year. His squad can easily cope in the Championship and whichever team he puts out will be more than formidable.”
Meanwhile, left-back Joe Mattock insists that he and his team-mates will relish their underdog status ahead of this evening’s tie – and believes that causing a shock would provide a big confidence booster for the Millers’ league programme.
He said: “The gaffer has said it and we can think it. We like being the underdogs and are not going to go there and look pretty.
“We are there to get a result and we want to beat them.
“There is no doubt that as a team, we can take it to them. We have got to go there on the front foot. They are obviously a Premier League team and a good side, but there is no doubt we can go there and nick a win.
“If you can nick a result and cause an upset, it can build massive confidence going on into the league games.”
Warne revealed he is still hoping to bring in at least one new signing before Friday’s loan deadline, with Brighton midfielder Richie Towell remaining a leading target.
Last six games: Everton WDLDWD; Rotherham LWWLLW.
Referee: G Scott (Oxon).
Last time: Everton 3 Rotherham 0, October 7, 1992; League Cup.