Few studies in the open literature have studied the effect of thermal barrier coatings when used in combination with shaped hole film cooling and enhanced internal cooling techniques. The current study presents RANS conjugate heat transfer simulations that identify trends in cooling design performance as well as experimental measurements of overall effectiveness using a flat-plate matched-Biot number model with a simulated TBC layer of 0.42D thickness, where D is the film cooling hole diameter. Coolant is fed to the film cooling holes in a co-flow configuration, and the results of both smooth and rib-turbulated channels are compared. At a constant coolant flow rate, enhanced internal cooling was found to provide a 44% increase in spatially-averaged overall effectiveness, , without a TBC. The results show that the addition of a TBC can raise on a film-cooled component surface by 47%. The optimum velocity ratio was found to decrease with the addition of enhanced cooling techniques and a TBC as the film provided minimal benefit at the expense of reduced internal cooling. While the computational results closely identified trends in overall system performance without a TBC, the model over-predicted effectiveness on the metal-TBC interface. The results of this study will inform turbine component design as material science advances increase the reliability of TBC.