Lampard has gone from strength to strength in the last year and has stepped up from being seen as an England fringe player to one worthy of a starting place - he earned his 11th cap against Liechtenstein on Wednesday.
That's no surprise to Jamie. "To me, Frank has always been a really, really good player but it's only now that he's starting to get the credit he deserves," said the skipper.
"He's moved to a new club and perhaps at West Ham he was stuck in the shadow of his dad and my dad as well and that didn't help him
"But he's come on since his move and now he's as good a midfielder as we've got in the country and playing regularly for England.
"He's got just about everything. He's an all-round midfielder who got a great shot on him, he's quick, can tackle, good long passing game, it's just about all there. I'm really pleased for Frank because he's come on a bundle."
Jamie revealed that the pair get on well and speak regularly. "I spoke to him the other day to wish him well before the England game and we get on well and vice-versa, when things are going well for me he's the first to contact me, as he did when he found out that I'd become Tottenham captain.
"We're both there for each other and want each other to do well because we both know how much football means to us."
So what about that bone-crunching 50-50 on Saturday? "Frank would want to win it and I'd want to win it," insisted Jamie. "It was the same last season when he had a good tussle at White Hart Lane in the 0-0 game and I thought we deserved to win that game as well."
Jamie Redknapp is preparing for another battle with his cousin Frank Lampard - a player he believes is finally getting the credit he deserves.