Processes for producing a component containing a ceramic-based material and having detailed features formed from materials other than ceramic materials. Such a process entails producing the component to include a first subcomponent and at least a second subcomponent having at least one off-axis geometric feature that results in the second subcomponent having a more complex geometry than the first subcomponent. The first subcomponent is formed of a ceramic-based material, and the second subcomponent and its off-axis geometric feature are separately formed of a metallic material and attached to the first subcomponent to yield a robust mechanical attachment. The component may be, for example, a gas turbine airfoil component.