I think it is safe to say that Jack Nicklaus was one of the most clutch putters in the history of the game. If you watch old footage of Jack in the majors, he is draining miles of putts, and a lot of them happen to come at very critical moments in the tournaments. I came across this tip Jack was quoted saying:
"When I putt, I hold my breath just before initiating the stroke to keep my head and body still."
How great is that? This is so simple and easy, it makes you wonder why you never thought of it on your own. Its because a lot runs through your mind on the putting green and these type of details are forgotten.
Keep this tip in mind, practice it and turn it into a habit. After a while you won't have to remember it, it will come naturally and so will an improvement in your putting.