A ceramic coating for imparting one or more of a variety of functional characteristics (e.g., reducing vibration levels) to one or more components or portions of an engine (e.g., ring segments, transition ducts, combustors, blades, vanes and shrouds of a turbine engine, portions thereof, and portions of a diesel engine), the components or portions comprising such a coating, and methods of making same. The ceramic coating exhibits a gradient or other change in the functional characteristic(s) through the thickness of the coating, across the surface area of the coating or both.