One of the rules of putting technique which I like all my students to follow is that if it does not need to move then it should not move. What I mean by this is that the wrists, the elbow joints, the arms from the shoulder joints the hip joints, or any part of your body that does not need to move should not move.
How to Keep Your Shoulders Still While Putting
Keep the putting stroke as simple as possible. A little drill which is very common and one that everyone can benefit from is to take your golf umbrella and put it under your arms just above your elbows trapped against your body. From here without the putter just practice rotating your body and shoulders around the axis of your back. Feel the shape of your arms and shoulders staying intact so that there is no movement from the wrists, elbows or arms from the shoulders.
Master the Pendulum Motion
Once you have the feel of that nice pendulum motion, take your putter and set up to a few balls. Start hitting some putts feeling that your shoulder move your arms, and your arms move your hands and your hands move the putter. You get a lovely feeling of a pendulum stroke with no hip movement. Another little tip is to make sure that the through stroke is a little longer than the backstroke, which will make sure the putter head is accelerating. This is a great drill to get the feel of nice simple pendulum putting stroke.