  We systematically examine uncertainties from fitting rare earth single-ion
crystal electric field (CEF) Hamiltonians to inelastic neutron scattering data.
Using pyrochlore and delafossite structures as test cases, we find that
uncertainty in CEF parameters can be large despite visually excellent fits.
These results show Yb$^{3+}$ compounds have particularly large $g$-tensor
uncertainty because of the few available peaks. In such cases, additional
constraints are necessary for meaningful fits.
