A common indicator of rheological dysfunction is a measurable decrease in the deformability of red blood cells (RBCs). Decreased RBC deformability is associated with cellular stress or pathology and can impede the transit of these cells through the microvasculature, where RBCs play a central role in the oxygenation of tissues. Therefore, RBC deformability has been recognized as a sensitive biomarker for rheological disease. In the current study, we present a strategy to measure RBC cortical tension as an indicator of RBC deformability based on the critical pressure required for RBC transit through microscale funnel constrictions. By modeling RBCs as a Newtonian liquid drop, we were able to discriminate cells fixed with glutaraldehyde concentrations that vary as little as 0.001%. When RBCs were sampled from healthy donors on different days, the RBC cortical tension was found to be highly reproducible. Inter-individual variability was similarly reproducible, showing only slightly greater variability, which might reflect biological differences between normal individuals. Both the sensitivity and reproducibility of cortical tension, as an indicator of RBC deformability, make it well-suited for biological and clinical analysis of RBC microrheology.