A method of positioning a bearing of a turbomachine in a squeeze film annulus is disclosed. The method includes providing a bearing in which a rotor shaft is disposed and a bearing support mounted about and radially supporting the bearing, with the bearing support at least in part defining the squeeze film annulus. A further step typically includes providing a plurality of centering elements associated with the bearing and bearing support and acting to center the bearing within the squeeze film annulus, with the centering elements provided at radially spaced locations around the bearing. An additional step in the method may include individually machining or shimming the centering elements to adjust the positioning of the bearing in the squeeze film annulus or to impart pre-load to improve the resiliency of the centering elements.