Memorize all of your lines before ever stepping foot onto the film set. If you have several scenes to do in one day, memorize them in the order that you will be performing. In a close-up shot, it is very easy to see if you are searching for your lines. Preparation is extremely important.
Take your index cards and write down your dialog if you are having a difficult time memorizing your lines. Since a close-up shot is basically just you and your face, or upper-body, the other actors are not seen on camera. Tape the index cards with your lines (or hint words) onto the forehead of the actor you are working with. This will keep your eyes from having to move as if you are reading something, and it will appear to the camera that you are gazing into their eyes.
Monitor your movement during a close-up shot. You will not want to sway back-and-forth or do much moving of your head. A simple nod, or glancing down may not seem very powerful, but through the eyes of the camera, it is plenty. Too much movement can ruin a close-up shot.
Rehearse your facial expressions in the mirror prior to actually filming your close-up shots. You may think that you have to be over-emotional during a scene, however, with a close-up shot less is absolutely more. Internal acting is extremely important during a close-up, because if you become too external in your movements and facial expressions it will come across as fake and strange.
Review the material that the director has shot after every close-up. Make note of your facial expressions and if you, or the director, are dissatisfied with your performance, ask yourself what you can do to improve your emotional range within the scene. You may find that your movements are too large, or too small, and if this is the case, revise how you perform the scene to create a perfect close-up shot.