The accuracy of NMR-derived nuclear magnetic dipole moments is ultimately limited by the uncertainty of the corresponding NMR shielding constants. Here, using hydrated Tl[+] as a demanding heavy-ion test case, we show that NMR shielding uncertainties related to hydration-shell structure and electronic-structure approximations can be reduced to the QED scale. SCAN functional based machine-learning-force-field molecular dynamics captures the key experimentally known features of the Tl[+] hydration structure, while coupled-cluster-calibrated four-component Dirac–Kohn–Sham calculations provide the ensemble-averaged shielding with a controlled residual uncertainty. The resulting magnetic moments of [203]Tl and [205]Tl are 1.6198(3)µN and 1.6357(3)µN, respectively. These values eliminate a systematic error of order 10[−][3]µN and reduce the residual uncertainty to the 10[−][4]µN level. Our workflow provides a transferable route to high-accuracy NMR-derived moments of heavy nuclei used as reference quantities in atomic and nuclear physics.