The King and Queen Consort met the singer when they visited the venue in Liverpool and unveiled the event's set.
Camilla said "no pressure" to Muller, who replied: "It feels like a good energy this year, no nil points."
She added: "As long as I can get up there and say it's the best I've ever done it, I'll be pleased."
The venue will stage the first semi-final in less than two weeks, as the UK hosts the annual competition on behalf of last year's winners Ukraine.
The grand final will take place a week after the coronation.
"We'll be watching with great interest, egging you on," the King told Muller.
The King and Queen Consort also met co-hosts Hannah Waddingham and Julia Sanina, commentators Rylan Clark and Scott Mills, and members of the production team.
"They were very lovely, so chatty," Clark told BBC Radio 2 afterwards. "And Queen Consort Camilla was like, 'I hear you've been in The Archers," referring to his appearance in a special Eurovision episode of the Radio 4 soap.
Clark went on to tell the King he would have to "behave himself this year" because Eurovision is in the UK, Mills said. "I won't be able to roll around Italy like I normally do," Clark added.
"That did get a Royal laugh," noted Mills.
The King and Queen Consort also pushed a button to officially light up the arena for the first time.
The venue has been fitted with more than 2,000 specialist lighting fixtures, with a pink, blue and yellow colour scheme to match this year's Eurovision logo.
The cabling for the lighting, sound and video could reach eight miles if rolled out.
Around 6,000 fans will be in the arena for each of the shows, with an estimated 160 million viewers watching the final around the world.
Tickets have sold out, but there will be a Eurovision Village fan zone for thousands to watch the event on big screens, and a two-week cultural festival in the city will also run alongside the competition.
BBC director general Tim Davie said: "It is an honour that His Majesty The King and Her Majesty The Queen Consort have come here today to reveal the fantastic staging for our Eurovision Song Contest programming.
"This set will be the focal point for all of the celebrations and we cannot wait to see it lighting up Liverpool and TV screens across the world."
Last month, stage designer Julio Himede told the BBC's Eurovisioncast podcast the set at the M&S Bank Arena was "very adaptable".
"It was an interesting creative challenge to come up with a design that felt big enough in the arena and big enough on camera," he said.
"Creatively, me and my team had to think about how we could give the stage an identity that says Eurovision - one of the biggest music shows in the world."
Around half of the 37 participants wil use the catwalk that extends from the main stage during their performances, he added.
As this year's host broadcaster, the bulk of the cost to put on the three live televised shows falls to the BBC.
The total is expected to be between £8m and £17m, but the corporation hasn't released its budget for the event.
Each year, the 37 competing broadcasters all pay a fee to enter, which in recent years has totalled a combined sum of about £5m.
The BBC, which is the UK's participating broadcaster, does not make its contribution public.
There is also £10m coming from the UK government, which includes an undisclosed amount being given to assist with the BBC's spending for the event.
However, officials say the majority will be spent on ensuring "the inclusion of Ukrainian culture".
Finally, local authorities in Liverpool have pledged £4m for the event.