A component includes a substrate that has outer and inner surfaces. The inner surface defines at least one hollow, interior space. The outer surface defines pressure and suction sidewalls that are joined together at leading and trailing edges of the component and together form an airfoil portion of the component. The outer substrate surface further defines at least one platform and at least one fillet that extends between and integrally connects the airfoil to the respective platform. The outer surface defines one or more grooves that extend at least partially along a respective fillet. Each groove is in fluid communication with a respective hollow, interior space. The component further includes a coating disposed over at least a portion of the outer substrate surface and including at least a structural coating that extends over the groove(s). The groove(s) and the structural coating together define channel(s) for cooling the respective fillet.