The 26-year-old has not always seen his value recognised at Emirates Stadium, with unfortunate injuries having stunted his progress at times.
Ramsey has, however, now passed 300 appearances for Arsenal and remains a key part of Arsene Wenger’s plans.
The Gunners boss has billed the midfielder as a possible candidate to succeed Per Mertesacker as skipper at Emirates Stadium, and Coleman has suggested he is ready for that responsibility.
He said: "I tried to take the pressure off him [by removing him as Wales captain] because a lot of things had changed. So I went to Arsenal's training ground to talk to him and he was brilliant.
"He could have spat his dummy out because he is a great player for us, but he was absolutely fantastic.
"He accepted it and I'm not surprised by Arsene's comments about him being a future Arsenal captain."
Coleman believes Ramsey will step back into a leadership role with his country at some stage, with his quality and mental toughness having shone through alongside fellow star turn Gareth Bale.
"Whether I am a manager or not I see him as the Wales captain again in the future," added the Wales coach.
"I told him that when I took the captaincy off him because he's got that about him.
"Mind you, he's in good company with Gareth Bale and Chris Gunter with his experience.
"He's not had an easy ride at Arsenal, he's had a lot of criticism and it's the same with Gareth at [Real] Madrid
"Aaron has come out with his sleeves rolled up and thought 'I am going to show those who doubt me.' He keeps on doing that again and again."