Norrie is through to the last 32 for the first time and will take on the eight-time champion.
British number two Norrie continued his brilliant season by beating Alex Bolt to reach the last 32 at the All England Club for the first time.
He is yet to go further, and will of course be the underdog against eight-time champion Federer, who was much improved against Richard Gasquet on Thursday, but there are several reasons to believe the 25-year-old could spring an upset.
Smith, Britain’s Davis Cup captain and the Lawn Tennis Association’s head of men’s tennis, told the PA news agency: “He will believe he can win and he has to believe that.
“He’s going to have to play a great match, that’s obvious, but the way he’s playing – there’s a reason why he’s number 12 in the race rankings this year.
“He knows he’s fit enough; if he needs to go five sets with him, he can go five sets. He’s just got to go out and make it as difficult as possible and make it as physical as possible – I think that’s really important for him.
“He’s played on big courts, he’s more used to those environments, which is great. He’ll get great support. It’s great for him. He deserves opportunities like this.”
Since the start of 2021, Norrie has reached the third round at both the French and Australian Opens, made three ATP Tour finals, including on grass at Queen’s Club, and beaten five top-20 players.
His ranking has climbed from 74 to 34, while his performances over the year so far put him close to the top 10 in the annual standings.
Norrie does not have a particularly big serve or a standout shot, with his rise built on supreme fitness and athleticism and a relentless approach to each point.
Highlighting what makes Norrie such a difficult opponent, Smith said: “His weapons are different. His weapons are his mindset, his operating standards, work ethic.
“His actual game is really effective. He’s improved it. I watched courtside at Queen’s and I was really impressed. His ball speed’s gone up this year, his forehand is way more offensive, he’s taking the ball earlier.
“The fact that his forehand is naturally quite spinny, and him and (Adrian) Mannarino are probably joint equal with the flattest backhands, I think the opponent gets such a different shot each time that it’s actually quite difficult to find a rhythm against Cam, and ultimately one of his weapons is he makes the opponent miss because of that.
“His serve’s improved and the other weapon he’s got is he plays every single point on merit. He eats away at opponents. It’s a great maturity he’s got now. And obviously the physicality he now brings.
“He’s so fit that he can play every single week. And what an advantage that is. I think all those things contribute to what he’s doing this year.”
Norrie, who was supported through the LTA’s Pro Scholarship Programme for the best British players aged 16-24, has experience of taking on the big guns, having played Rafael Nadal in both Melbourne and Paris this year.
He was beaten in straight sets both times but not without making an impression, and Smith added: “He’s beating really good players now. Because he’s going deeper, he’s playing better players more often, and that’s raising his level.”
The LTA has answered more than its fair share of awkward questions after poor first weeks for British players at Wimbledon, but that has certainly not been the case this year.
Norrie was one of three British men along with Dan Evans and Andy Murray to reach the last 32, the best this century, while 18-year-old Emma Raducanu has announced her talent to the world in the women’s draw.
Smith coached Murray as a teenager and has sat in the stands for nearly all of his fellow Scot’s big Centre Court moments.
He was courtside for Murray’s first two matches against Nikoloz Basilashvili and Oscar Otte, where the 34-year-old came from two sets to one down to thrill the passionate crowd.
“It’s one of my favourite atmospheres I’ve ever been in, and I’ve been in a lot with Andy,” said Smith.
“Because of what he’s gone through, I found it really emotional watching it and got really fired up. I just loved the atmosphere, I thought that was great for tennis.
“Him, his family, his team, the ups and downs they’ve had to go through – and there have been so many setbacks – but two occasions like he’s had will make him feel that the hard work and the commitment, that’s what it’s for. And it will fire him up to have more of these – I hope it’s many more.”