X-ray computed tomography (CT) is widely used in material science to understand the inner morphology of a specimen. Often, it is used to qualitatively understand the distribution of salient features such as cracks, voids, or particles. There are many challenges in using X-ray CT in a quantitative manner. These include a coarser resolution for comparable fields of view when compared to other imaging techniques (i.e., electron or optical microscopy), imaging artifacts (i.e., beam hardening and phase contrast), and the plethora of imaging and processing parameters that are chosen by the instrument/software user that can significantly affect the resultant measures. These limitations must be considered and quantified to acquire accurate and precise measurements. X-ray CT is powerful in that it can measure, in three dimensions, salient features that are subsurface and cannot be imaged with other direct line-of-sight imaging techniques. In this work, we discuss the use of X-ray CT to measure the thickness variations of thin walls of opacity capsules as well as the measurement of double-shell targets to understand the concentricity of the capsules within each other. Morphological measurements needed for target characterization require very high accuracy and precision. This paper will describe the application for the first time of a variety of measurements and will explore their robustness and pros and cons to identify areas of research to improve their accuracy and precision.