Despite the large known chemical shift (CS) range for boron and the large number of B-11 NMR studies of glasses, no boron CS tensors have been characterized to date. We report the application of solid-state NMR techniques at moderate (9.4 T) and high (17.63 T) applied magnetic field strengths to the characterization of the boron CS tensors in trimesitylborane (BMes(3)) and triphenyl berate (B(OPh)(3)). The boron CS tenser of the former compound exhibits a remarkably large span, Omega = 121 +/- 1 ppm, which encompasses the known range of isotropic chemical shifts for tricoordinate boron compounds. Conversely, the effect of the boron CS tenser on the B-11 NMR spectra of B(OPh)(3) is difficult to observe and quantify even at field strengths as high as 17.63 T; we find Omega less than or equal to 10 ppm. This marked difference in the boron nuclear magnetic shielding tensors is reproduced accurately by a series of ab initio and DFT calculations with a range of basis sets. The difference is rationalized in the context of Ramsey's theory of nuclear magnetic shielding by considering contributions to the paramagnetic shielding in the tricoordinate boron plane. Differences in the in-plane shielding tenser components for the molecules considered are a result of variations in the effectiveness of the mixing of occupied a orbitals with virtual pi orbitals under the influence of an applied magnetic field. A similar explanation has been invoked to rationalize C-13 isotropic chemical shifts in classical and nonclassical carbocations. We also report experimental and calculated boron nuclear quadrupolar coupling constants and asymmetry parameters for BMes(3) and B(OPh)(3). A combination of experimental and theoretical results provides the orientation of the CS and electric field gradient tensors in the molecular framework.