Gas-phase NMR spectra of (11)B, (10)B, and (19)F in BF(3) are reported, and high-level ab initio calculations of the corresponding NMR shielding constants are described. Extrapolation of the measured resonance frequencies to the zero-density limit ensures that the results correspond to the ab initio values for an isolated molecule. Simultaneous measurements of (3)He resonance frequencies and application of the calculated shielding constants allow us to determine improved values of the nuclear magnetic dipole moments of (11)B and (10)B. The magnetic moments of both isotopes are also determined independently by comparing with the (19)F spectral parameters (frequencies and shielding constants). The separately derived nuclear magnetic moments are in good agreement, whereas the literature moments of both (11)B and (10)B are noticeably less accurate.