Will one always get better chemical shift resolution at higher field? You may be surprised to learn that the answer is - no. In certain cases for liquids, where dynamic processes are occuring at a rate comparable to the frequency difference between resonances (i.e. on the NMR time scale) one may even get less resolution at higher fields due to line width changes at higher field.
In the MAS or CPMAS spectra of solids one obtains liquid-like spectra of solid materials. In the cases where dipolar coupling is effectively removed by either or both MAS and high power decoupling, the width of the resonances often depends on a chemical shift distribution associated with a particular site. Just like chemical shielding anisotropy, this distribution increases (in Hz) with the magnetic field strength. As a result, the chemical shift resolution does not improve on going to higher field as the widths of the MAS lines increase (in Hz) as a function of field. Two examples of this are shown below. The first figure is the 29Si CPMAS spectrum of the clay kaolinite at 11.7 T (top trace) and 21.1 T (bottom trace). Both spectra were acquired with MAS rates exceeding the span of the chemical shift tensors. One can see that there is little if any improvement in the chemical shift resolution at higher field.
The second figure is the 19F MAS spectrum of the perfluorinated polymer, Nafion at 11.7 T (top trace) and 21.1 T (bottom trace). The MAS rates for each spectrum were chosen such that the dipolar coupling between the fluorines was effectively averaged by the MAS and that the spinning sidebands would be coincident (in ppm) in the spectra. Again, one can see that there is little if any improvement in the chemical shift resolution at higher field.
Thank you to Victor Terskikh and Eric Ye of the National Ultrahigh-Field NMR Facility for Solids for providing the figures for this post.