It was compliments all round as the New England Patriots came face-to-face with the Los Angeles Rams ahead of their Super Bowl showdown.
The teams were out in Atlanta for the Super Bowl Opening Night, where players and coaches rubbed shoulders and spoke to the media before the final on Sunday (Monday morning UK time).
Belichick, 66, is twice McVay's age and already has five titles under his belt.
Widely considered one of the greatest coaches in NFL history, the Patriots chief heaped praise on his younger rival, saying the Rams are "very well coached" and can "play in all situations".
He told the NFL Network: "They scored 527 points this year and they can certainly move the ball and score points against everybody.
"They can run it, they can throw it, they can throw it deep, they can catch and run, they have a very good offensive line that's played together in every game so they have a lot of consistency and continuity there.
"Coach McVay has a good system; he communicates well with the quarterback and the quarterback makes good decisions. So, when you put all of those things in place its easy to see why they've scored as much as they have."
McVay was similarly full of plaudits for Belichick, who has previously led the Patriots into eight Super Bowls.
He said Belichick had contacted him by text after games during the season to congratulate him on the Rams' performance.
"For him to even take the time to text me after a game, it means a lot because of the respect I have for him. He's been doing it at such a high level for so long and it means a lot," McVay told the NFL Network.
"You respect your peers and he's somebody I have a lot of respect for."
The Patriots last won the Super Bowl in 2017 and made it to the final again in 2018, but lost to the Philadelphia Eagles.
The last time the Rams were in a Super Bowl was in 2002, then the St Louis Rams, when they lost to the Patriots.
The Rams, then known as the Greatest Show on Turf, went into the game as favourites but were stunned by a New England side who were forced to bring in a young, untested Tom Brady part way through the season and won the game 20-17.
Victory would serve as a launchpad for Patriots success, having won the AFC Championship eight times and Super Bowl on four occasions since.
Despite the teams' different fortunes in recent years celebrated quarterback Brady is under no illusions about the challenge awaiting the New England.
"They've got a great team, I've got to go against that guy all night (Rams cornerback Aqib Talib) which I'm concerned about," Brady told the NFL network.
"I know how great of a player he is, they've got a great defence – the best D-line in the league, a couple of the best interceptors that ever played in this game. So I've got my work cut out for me."