Third seed Murray plays Italian 25th seed Andreas Seppi in the third match on Centre Court at around 17:00 BST.
Ward, ranked 110th, takes on Canada's Vasek Pospisil in the second match on court one at around 15:00.
"It's great for British tennis and it's great for everyone involved that more people are winning matches and doing well," said Ward.
"I've got to worry about my match. Andy worries about his."
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Murray, 28, practised with Ward on Friday and the pair have become good friends over the past two years.
"We've done a few training blocks together," said the Scot. "He stayed with me in Miami a few times.
"I watch a lot of his matches online when he's playing challengers and stuff. I kind of say, 'Well done,' or let him know what I thought about the match, anything like that. See if I can help in any way."
Ward is through to the last 32 of a Grand Slam for the first time and the 28-year-old Londoner has ensured he will break into the world's top 100 for the first time in the next rankings.
He will face 25-year-old Pospisil, the reigning Wimbledon doubles champion, for the first time at the top level.
"I know him pretty well," said Ward, who will collect at least £77,000 in prize money.
"He's a good friend of mine actually. We spend a lot of time together. In the last few years, we've played a couple of times as well in the Challenger tour, a couple bigger matches in the semis and finals in the past.
"We both know each other's games, so there's not too many secrets. As I say, it's a great chance for both of us."
Murray has won six of his seven matches against Seppi, the only defeat coming on grass in Nottingham eight years ago.
The 31-year-old Italian has reached two finals this year and beat Roger Federer at the Australian Open in January.
"He has had such good results this year," said Murray. "He made the final a couple of weeks ago in Halle, plays well on the grass.
"He won against Roger at the Australian Open this year. He's capable of playing some top tennis."
Andy Murray will have friend and fellow Briton James Ward for company in the third round of Wimbledon on Saturday.