A centering ring may be used to provide a resilient mounting system with uniform stiffness for rotating machinery. The centering ring may have first and second exterior raised ridges on one surface and a central raised ridge on the other surface. The centering ring may be disposed between the housing of the rotating machinery and a bearing provided therein. Due to its uniform cross-sectional geometry about its entire circumference, the centering ring may provide uniform stiffness in any radial direction. The centering ring may be useful in any rotating machinery, including generators, turbo machines and turbine engines.