The industrial use of X-ray Computed Tomography (known briefly as XCT, or sometimes simply as CT) is on the rise because a single XCT scan can measure an arbitrary number of features, and XCT instruments can measure features inaccessible to contact or optical instruments — even features that are completely encased in material. This makes XCT a natural metrological companion to additive manufacturing where internal features (e.g., lattice structures) can be produced. But this advantage of being able to measure through material is somewhat mitigated by the fact that the obstructing material has a strong influence on the geometric measurement and is a dominant source of error. This problem is addressed by two emerging documentary standards in ASME and ISO (International Organization for Standardization). These documents define standardized tests for metrological accuracies of an XCT system, where accuracies — now unambiguously defined — can be expressed as Maximum Permissible Errors (MPEs). These tests rely on calibrated artifacts that are designed to reveal various XCT error sources when the system measures these artifacts in prescribed manners. This paper gives the general philosophy behind Coordinate Measuring System standards and then applies them to XCT systems in particular. Rationale is given for the artifact choices contained within these standards, with particular emphasis on material effects, and clarifies the metrological coverage of these standards.