Medvedev was outplayed by 37-year-old Federer to crash out of the Masters 1000 event on Wednesday.
The match – delayed by a day due to bad weather – saw Federer run out a comfortable 6-4 6-2 victor.
Medvedev was powerless to prevent the Swiss maestro romping to a second straight-sets victory of the tournament so far.
It was Federer’s third career win over Medvedev and the Russian was all praise for his opponent after the match.
Medvedev clipped a forehand wide to hand Federer the match on the Miami hard court and sent a message to the Swiss at the net.
When the pair shook hands, Medvedev said “good luck” to the 20-time Grand Slam champion, before tapping him twice on the chest.
Roger Federer smiled before shaking the match umpire’s hand and then throwing his sweat band into the crowd.
Federer plays Kevin Anderson in the Miami Open quarter-final today as he guns for a 101st ATP title.
The Swiss tennis maestro lost the Indian Wells final to Dominic Thiem two weeks ago.
Federer is now the favourite to win the Miami Open after Novak Djokovic was knocked out overnight.
And he revealed his gameplan for how to overcome Anderson.
“I think it’s going to be a bit tricky,” he said.
“He’s got a great serve, so you go back to big-serve mentality to try to hold your own service games first before thinking about how to break Kevin.
“Had a tough one against him at Wimbledon when I lost.
“Was able to come back and play a good match against him in London when I really had to in that round-robin match.
“But, you know, I think I’m feeling really good.
“Today’s match I can be really happy with. I hope it’s going to give me some confidence for tomorrow.”