Integral benchmarks for criticality safety and nuclear data validation require expensive uncertainty quantification studies. In general, uncertainty quantification techniques ignore correlations between experiments and shared components. Experiments, such as the Thermal/Epithermal eXperiments (TEX) campaigns, consist of many shared components, such as the Jemima highly enriched uranium (HEU) fuel plates, which create a strong correlation in their uncertainties. While these correlations are known to exist, they are often not estimated because of the complexity of such calculations. This paper describes an intuitive method of determining the covariance for each of the experimental components, providing a correlation for each family of components across the multiple cases examined within a benchmark. A proof-of-principle study using the TEX-HEU experimental campaign was performed and verified that the covariance and correlation matrices can be calculated with information commonly found in the International Criticality Safety Benchmark Evaluation Project benchmarks. This study showed that the introduction of model and experimental covariances reduces the χ2 per degree of freedom from 2.203 to 1.179, indicating that the omission causes overly pessimistic bias quantifications. This technique can be seamlessly integrated to current benchmark evaluations as well as reevaluations of legacy benchmarks.