The stoichiometric calibration method for dual‐energy computed tomography (DECT) can be used in geosciences to characterise materials based on their effective atomic number (Zeff) and their electron density (ρe) without previous knowledge of the incident X‐ray beam. A stoichiometrically calibrated DECT method was applied here to measure these two properties on three different sedimentary rocks using three different X‐ray CT instruments to determine which one is best to reveal the chemical composition or the mineralogical variations at the meso‐scale. The three tested instruments: (1) a medical CT, (2) a custom‐built micro‐CT, and (3) a commercial micro‐CT. Several acquisition settings were tested to identify the most suitable parameters for the characterisation the samples. Some parameters such as incident energies, resolution and calibration materials proved to have a significant impact on the accuracy of the characterisation. The determination of a general measurement protocol for geological samples was found to be difficult because of several complicating factors, including the nature of the sample, objectives of the study, and instrumental limitations that influence DECT characterisation. Nonetheless, comparison of the results obtained by the three scanners brings out the key parameters to be considered to perform a useful rock sample characterisation with DECT.