A spot in the Women's Asian Cup decider will be on the line when Australia - ranked 15th in the world - and No.17 China lock horns in a blockbuster semi-final at the 60,000-seat Optus Stadium.
Montemurro, who has been at the helm of Australia for nine months, and Milicic have traded compliments in the lead-up.
Milicic is a former coach of the Matildas who led them to the Round of 16 at the 2019 Women's World Cup, but he's been in charge of China since 2024.
Other aspects of his impressive resume include being an assistant coach to Ange Postecoglou at the Socceroos, an assistant to Tony Popovic at Western Sydney, and being Macarthur's inaugural head A-League Men coach.
"I have the utmost respect for Ante as a person and as a student of the game," Montemurro said of Milicic, who has also led the Australian U23 and U20 men's sides.
"He sees the game holistically, but sees the game for the reality that it is.
"I think that he's one of the special coaches that's been produced in Australia."
The Matildas will start as hot favourites on home soil for the semi-final, but defending champions China can't be dismissed, despite entering the match without suspended star Wang Shuang.
Montemurro is preparing himself for a Milicic tactical special.
"We could talk about the football on the pitch, but there's also going to be a tactical battle that I need to be prepared for off the pitch," Montemurro said.
"I know he's going to throw some things at us."
Milicic has been equally full of praise for Montemurro, who was previously coach of European women power clubs such as Arsenal, Lyon and Juventus.
"What he's done for the women's game, being an Australian coach, is incredible," Milicic said.
"He's coached a few massive clubs in Europe, and I'm delighted that he's in charge of the Matildas, because they've got a coach with plenty of experience that knows the girls.
"When we had the Asian Cup draw here in in July, we spent a lot of time there together, so it's a good friendship, it's a strong rivalry, and I'm sure that on Tuesday night both of us will be looking for the victory."
In a major boost to Australia's victory hopes, vice-captain Steph Catley and star winger Hayley Raso passed their concussion tests.
Australia looked vulnerable in their 2-1 quarter-final win over North Korea, conceding 21 shots to four and having just 38 per cent possession.
Montemurro is imploring his side to adopt a more possession-based game plan against China.
