The first monochromatic X‐ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X‐ray energies. In order to quantitatively account for the experimental values obtained for the Hounsfield (or CT) number, it was necessary to consider various issues including the point‐spread function for the X‐ray imaging system and harmonic contamination of the X‐ray beam. The analysis and interpretation of the data includes detailed considerations of the resolution and efficiency of the CCD detector, calculations of the X‐ray spectrum prior to monochromatization, allowance for the response of the double‐crystal Si monochromator used (via X‐ray dynamical theory), as well as a thorough assessment of the role of X‐ray phase‐contrast effects. Computer simulations relating to the tomography experiments also provide valuable insights into these important issues. It was found that a significant discrepancy between theory and experiment for the Cu wire could be largely resolved in terms of the effect of the point‐spread function. The findings of this study are important in respect of any attempts to extract quantitative information from X‐ray tomography data, across a wide range of disciplines, including materials and life sciences.