In the power plant industry, the turbine inlet temperature (TIT) plays a key role in the efficiency of the gas turbine and, therefore, the overall — in most cases combined — thermal power cycle efficiency. Gas turbine efficiency increases by increasing TIT. However, an increase of TIT would increase the turbine component temperature which can be critical (e.g., hot gas attack). Thermal barrier coatings (TBCs) — porous media coatings — can avoid this case and protect the surface of the turbine blade. This combination of TBC and film cooling produces a better cooling performance than conventional cooling processes. The effective thermal conductivity of this composite is highly important in design and other thermal/structural assessments. In this article, the effective thermal conductivity of a simplified model of TBC is evaluated. This work details a numerical study on the steady-state thermal response of two-phase porous media in two dimensions using personal finite element analysis (FEA) code. Specifically, the system response quantity (SRQ) under investigation is the dimensionless effective thermal conductivity of the domain. A thermally conductive matrix domain is modeled with a thermally conductive circular pore arranged in a uniform packing configuration. Both the pore size and the pore thermal conductivity are varied over a range of values to investigate the relative effects on the SRQ. In this investigation, an emphasis is placed on using code and solution verification techniques to evaluate the obtained results. The method of manufactured solutions (MMS) was used to perform code verification for the study, showing the FEA code to be second-order accurate. Solution verification was performed using the grid convergence index (GCI) approach with the global deviation uncertainty estimator on a series of five systematically refined meshes for each porosity and thermal conductivity model configuration. A comparison of the SRQs across all domain configurations is made, including uncertainty derived through the GCI analysis.