Certified reference materials (CRMs) enable the meaningful comparison of measurement results over time and place. When CRMs are used to calibrate or verify the performance of a measurement system, results produced by that system can be related through the CRM to well-defined, stable, and globally accessible reference(s). Properly done, this directly establishes the metrological traceability of the results. However, achieving the meaningful comparison of results from measurement systems calibrated and/or verified with different CRMs requires that the different materials truly deliver the same measurand, that is, are "the same" within stated uncertainty except for differences in the level of the analyte of interest. We here detail experimental and data analysis techniques for establishing and demonstrating the comparability of materials. We focus on (1) establishing a uniform interpretation of the common forms of CRM uncertainty statements, (2) estimating consistent measurement system response uncertainties from sometimes inconsistent experimental designs, (3) using "errors-in-variables" analysis methods to evaluate comparability studies and novel graphical tools for communicating results of the evaluation to reviewing authorities and potential CRM customers, and (4) augmenting established comparability studies with new materials using measurements provided by the certifying institution. These experimental and data analytic tools were developed in support of the Joint Committee for Traceability in Laboratory Medicine's efforts to enhance the reliability of clinical laboratory measurements and are illustrated with potassium and cholesterol measurands of clinical relevance; however, these tools can be applied to any group of materials that deliver the same nominal measurand with stated value and uncertainty.