The Swiss will compete in the men's final for a 10th time on Sunday following a 7-5 7-5 6-4 triumph over the 2013 champion.
Yet while the scoreline suggests it was a relatively comfortable straight-sets win, Federer acknowledged he had needed to be at the top of his game - particularly in the opening set - to come out on top against Murray.
"I was clearly able to play very well from the start," said the seven-time Wimbledon champion.
"The beginning was always going to be an important part of the game. I had to save break point first, then I was able to start rolling on my serve. (I) played a great game to break.
"[It is] definitely one of the best matches I've played in my career.
"I don't remember point by point, but it was definitely really, really solid."
Federer will now go on to face Novak Djokovic in a repeat of the 2014 final at SW19.
The world number one came out on top in a five-set thriller last year, though Federer still has fond memories of the epic contest despite being on the wrong end of the result.
"For me, I don't really think about the match we played against each other last year," Federer added.
"I just remember it was unbelievably thrilling. The crowd really got into it.
"I'm just happy personally for myself to be back in a final. Whoever that's going to be against, it's always a big occasion.
"That [it] is Novak, the world number one, obviously adds something extra."