When you are putting, keep your eyes down (preferably focused on a spot behind the ball) and listen for the ball falling in the hole, especially on short putts.
So just relax, keep your eyes down, have confidence in yourself and make a good, smooth stroke.
franklygolf 
Frank, one of my favorite adages:
“You have two choices — you can listen for the putts to go in or you can watch them miss, whichever you like better.”