Fourth seed Cilic, victor in 2012, overpowered American teenager Stefan Kozlov 6-0 6-4 while Querrey, who triumphed seven years ago at the west London club, got the better of Australian Jordan Thompson, winning 7-6 (3) 3-6 6-3.
He added: "It is tough to believe at 35 that I am playing my best tennis, but I think I am". Five years on he is hoping his opponent is sufficiently well behaved to last the match but unable to stem a run of success for the Croat that suggests even greater spoils on another London lawn across the River Thames might be attainable.
No matter the result in the championship match, both players will likely be pleased with their preparation heading into Wimbledon, tennis' premier grass-court event, whose main-draw matches get under way on July 3.
Cilic became the first player to break Muller in the tournament despite a barrage of 22 aces from the world number 26 and hammered down 20 aces of his own to return to the Queen's final for the first time since 2013.
Cilic failed to convert his opportunities in the second set, however, and one lapse of concentration at 5-6 blotted his copybook to allow Muller to snatch the second set.
The tournament had seen the top three seeds Andy Murray, Stan Wawrinka and Milos Raonic all uncharacteristically falling by the wayside in the first round. Then, at the third time of asking, crowd favourite Lopez could celebrate after fourth seed Cilic pulled a forehand into the tramlines.
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Lopez, who reached the final of another Wimbledon tune-up a week ago in Stuttgart, was out-aced 16-4 by Dimitrov but controlled his service games more effectively overall.
"I played him many times", said Lopez.
"I played great, I felt good from the start", said Federer.
Grigor Dimitrov, who won the title in 2014, also made it through after a mid-match hiccup against young Russian Daniil Medvedev who needed shoulder treatment after appearing to injure himself while practising his smashing.
Cilic kept Young under constant pressure, forcing the American to save 10 of 12 break points. "I have to keep it up with my level, with the way I'm playing, and wait for my chances".
Cilic wrapped up the opening set quickly and had he converted break points in the third or seventh games of the second set he would have spared himself any undue stress.