Beta decay asymmetry detected Nuclear magnetic resonance (β-NMR) is a spin magnetic resonance technique that uses radioactive beta-emitting isotopes as probes. Two of the main benefits of the technique are the wide selection of isotopes with different nuclear properties for the same chemical element and its high sensitivity. Traditionally this technique has been used for material science research to study internal electromagnetic fields of solid-state hosts, and for nuclear physics research to study how the electromagnetic moments change for different nuclei based on their proton and neutron distribution. This thesis expounds on the techniques and methods used to apply β-NMR to liquid state hosts. They are demonstrated by the determination of the magnetic dipole moment of ²⁶Na with ppm precision. The same steps can be used in the future for chemical, biochemical, and high-precision nuclear electromagnetic moment studies. Central to this measurement has been the magnetic field stabilization and measurement loop based on the NMR measurement of protons in water molecules. The implementation of which has been described in High-accuracy liquid-sample β-NMR setup at ISOLDE, Nucl. Ints. & Meth. A (1020), 2021, 165862 together with other adaptations of ISOLDE’s β-NMR-beamline. The method for measuring high-precision nuclear magnetic dipole moments as set forth in Magnetic moments of short-lived nuclei with part-per-million accuracy, Phys. Rev. X (10), 2020, 041061 contains the following elements. First, a measurement of the nuclear Larmor frequency with sub-kHz line-width. This has been achieved by using a room temperature ionic liquid (RTIL) as implantation host, reducing the spatial deviations of the magnetic field (homogeneity) to the ppm level by means of PCB shimming coils, and stabilizing the temporal fluctuations to the ppm level using a feedback loop. Second, an external reference and an accurate field map to determine the ratio of Larmor frequencies between the isotope of interest and the reference. Third, the same ratio for a stable isotope of the same chemical element in the same host material (a RTIL) with respect to the same reference. Fourth, a precise measurement of the Larmor frequency of the stable isotope. Fifth, an accurate NMR shielding constant for the environment in which the precise measurement of the stable isotope was performed, e.g. determined by ab initio NMR shielding calculations. Last, the chemical shift between chemical measurement environments used in the third and fourth steps. Combining these elements one can compute a very accurate magnetic moment of the stable isotope and use it to compute the magnetic moment of the isotope of interest by means of the chemical shift corrected ratio of Larmor frequencies. The result obtained for ²⁶Na is 2.849390(20) nuclear magnetons. This is in agreement with, but two orders of magnitude more precise than, the previous determination of the magnetic dipole moment of ²⁶Na. Because the magnetic dipole moments of ^{27 – 31}Na were determined by their ratio to ²⁶Na their magnetic dipole moments could be improved as well.