The development of a solid oxide fuel cell (SOFC) with a higher efficiency and power density requires an improved understanding and treatment of the irreversibilities. Losses due to the electronic and ionic resistances, which are also known as ohmic losses in the form of Joule heating, can hinder the SOFC’s performance. Ohmic losses can result from the bulk material resistivities as well as the complexities introduced by the cell’s microstructure. In this work, two-dimensional (2D), electronic and ionic transport models are used to develop a method of quantification of the ohmic losses within the SOFC anode microstructure. This quantification is completed as a function of properties determined from a detailed microstructure characterization, namely, the tortuosity of the electronic and ionic phases, phase volume fraction, contiguity, and mean free path. A direct modeling approach at the level of the pore-scale microstructure is achieved through the use of a representative volume element (RVE) method. The correlation of these ohmic losses with the quantification of the SOFC anode microstructure are examined. It is found with this analysis that the contributions of the SOFC anode microstructure on ohmic losses can be correlated with the volume fraction, contiguity, and mean free path.