This paper presents a case study of two selected beam hardening correction methods and their effects on dimensional measurements of multi-material objects. The methods under test are empirical cupping correction (ECC) and empirical dual energy calibration (EDEC). These methods were originally developed for medical applications and their potential for the reduction of artefacts is typically only analysed based on grey value images. For testing and benchmarking of the mentioned methods for dimensional metrology, a dedicated multi-material reference standard—a multi-material hole cube—is used. This reference standard was originally developed for acceptance testing of CT systems. This paper shows a second application of this standard. The reference standard has been calibrated by tactile measurements to assess centre–centre distance errors as well as patch-based bidirectional length measurement errors on beam hardening corrected data and on uncorrected data. For the application of the method also to industrial multi-material scenarios, slight modifications of the ECC method are proposed. Practical aspects of both the ECC and the EDEC approaches as well as measurement results are analysed and discussed in detail. ECC was able to significantly improve dimensional measurements and was especially able to reduce extreme errors occurring in particular in multi-material scenarios by a factor of more than 4. EDEC, the dual-energy approach, reduced grey value inhomogeneities caused by artefacts even more. Its performance for dimensional measurements was however a little worse than ECC. EDEC data resulted in a slightly larger total range of residual measurement errors, mainly due to an elevated noise level.