An experimental setup for consecutive measurement of ion and x-ray absorption in tissue or other materials is introduced. With this setup using a 3D-printed sample container, the reference stopping-power ratio (SPR) of materials can be measured with an uncertainty of below 0.1%. A total of 65 porcine and bovine tissue samples were prepared for measurement, comprising five samples each of 13 tissue types representing about 80% of the total body mass (three different muscle and fatty tissues, liver, kidney, brain, heart, blood, lung and bone). Using a standard stoichiometric calibration for single-energy CT (SECT) as well as a state-of-the-art dual-energy CT (DECT) approach, SPR was predicted for all tissues and then compared to the measured reference. With the SECT approach, the SPRs of all tissues were predicted with a mean error of (-0.84 ± 0.12)% and a mean absolute error of (1.27 ± 0.12)%. In contrast, the DECT-based SPR predictions were overall consistent with the measured reference with a mean error of (-0.02 ± 0.15)% and a mean absolute error of (0.10 ± 0.15)%. Thus, in this study, the potential of DECT to decrease range uncertainty could be confirmed in biological tissue.