The number one reason why amateurs miss short putts is deceleration. This symptom can creep up in many parts of your game, especially with chipping and putting. If you notice yourself stubbing chips and putts, or have trouble keeping those short ones on line, I would bet you even money you’re decelerating into impact. 
I cannot stress enough the importance of following-through to my students, I like to try and squash this fault as soon as possible. This simple move will help your short game tremendously as you no longer have to worry about potentially chunking or stubbing the shot. If you follow-through, the ball has nowhere to go but forward. If you start over-thinking things and try to steer your shots, the deceleration bug will creep in, and you’re game will suffer accordingly.
This is a simple drill I use to try and incorporate this simple fundamental into my students early in their lessons. I get them to putt to a hole about 5-10 feet away, but place a headcover / ball / range bucket in the way of their backswing to force them to keep it short. This forces them to accelerate into the ball and the results are immediate.
I would recommend everyone try this drill as you may not think you decelerate, however the results this drill produces may make you think otherwise. Don’t miss it.