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In order for the Department of Safeguards to provide credible assurance that states are honoring their safeguards obligations, quantitative conclusions regarding states' nuclear material inventories and activities are needed. The statistical analysis used to reach these conclusions requires that each measurement method undergo uncertainty quantification (UQ). This paper describes current work aimed at improved understanding of uncertainty sources and provides two example UQ applications, one using a top-down approach and the other using a bottom-up approach. We explore possible improvement of current top-down analysis, through a new calculation that accommodates multiplicative error models to compare operator and inspector data. To demonstrate the benefit of bottom-up analysis, we examine individual uncertainty components associated with uranium neutron coincidence collar (UNCL) measurements. Improving safeguards effectiveness is an on-going challenge and incorporating predicted uncertainties from bottom-up analyses into top-down verification measurement performance evaluations is a useful path forward to comprehensive UQ. [ABSTRACT FROM AUTHOR]