  A computational study of the Electron Paramagnetic Resonance (EPR)
$g$-tensors and hyperfine tensors of Li and Ga vacancies in LiGaO$_2$ is
presented. Density Functinal Theory (DFT) calculations are carried out of the
Ga and Li vacancies using the DFT+U approach in the charge states which carry
an unpaired spin. In both vacancies the hole is located on one oxygen
$p$-orbital adjacent to the vacancy. Apical and different basal plane O are
considered. The magnetic resonance parameters of the defects are determined
using the Gauge Including Projector Augmented Wave (GIPAW) method. The EPR
spectra of $V_\mathrm{Ga}^{2-}$ is characterized by a quasi-isotropic
superhyperfine (SHF) interaction with one Ga nucleus and for the apical O spin
gives a $g$-tensor with maximum oriented along the bond direction from that O
to its other Ga neighbor. For $V_\mathrm{Li}^0$ there is a quasi-isotropic SHF
interaction with two Ga nuclei and the $g$-tensor maximum is along ${\bf c}$
for the basal plane O spin. Both of these are in agreement with experiment but
we predict also the $g$-tensors for the other possible localization of the
spins as well as the small hyperfine splittings (as yet not observed) on Li.
The energies of formation and transition levels of the corresponding defects
provide insight into the conditions required to activate these EPR spectra.
