  Mott insulators with strong spin-orbit coupling display a strongly
anisotropic response to applied magnetic fields. This applies in particular to
Kitaev materials, with $\alpha$-RuCl$_3$ and Na$_2$IrO$_3$ representing two
important examples. Both show a magnetically ordered zigzag state at low
temperatures, and considerable effort has been devoted to properly modeling
these systems in order to identify routes towards realizing a quantum spin
liquid. Here, we investigate the relevant Heisenberg-Kitaev-$\Gamma$ model
primarily at elevated temperatures, focusing on the characteristic anisotropy
between the in-plane and out-of-plane uniform susceptibility. For
$\alpha$-RuCl$_3$, we find that the experimentally observed anisotropy,
including its temperature dependence, can be reproduced by combining a large
off-diagonal $\Gamma_1$ coupling with a moderate $g$-factor anisotropy.
Moreover, we study in detail the effect of magnetic dilution and provide
predictions for the doping evolution of the temperature-dependent
susceptibilities.
