A method of polishing an outer surface of a ceramic coated gas turbine engine component includes applying a rotating diamond brush to the outer surface. The brush is configured to achieve a uniform finish of 150 microinches Ra or less over the surface. The brush contains diamond impregnated bristles, and is affixed to a rotary head of a robotic arm. A force sensing controller limits brush forces against the component. The component disclosed is a hot section turbine vane designed for directional control of high temperature, high-pressure combustion gases, but the method may be applied to other components contained within such aerospace applications. The polished coating provides an improved thermal barrier for maintaining structural integrity of the component in environments having temperatures ranging up to 2,000 degrees Celsius. The method limits abrasive removal of ceramic material to only 0.0005 to 0.00075 inch, and saves time and expense over past practices.