Mathematical modeling is fundamental for interpreting measurements.  In order to leverage its full potential in metrology settings, however, one must understand how models relate to and inform uncertainty estimates.  Our current research addresses such problems by combining physics with tools from applied analysis, probability theory, asymptotics, optimization, and numerical methods to identify and quantify instrument-induced variability, inherent measurement uncertainty, and related concepts of uncertainty.  We work closely with experimentalists and stakeholders -- both internal and external to NIST -- to develop new measurement tools and improve quality of existing measurements.  Recent work has focused on (i) design and operation of microfluidic devices for cytometry and flow metrology, and (ii) optimization and interpretation of diagnostic tests for diseases such as COVID-19.