  A comprehensive set of muon spin spectroscopy and neutron scattering
measurements supported by ab-initio and model Hamiltonian simulations have been
used to investigate the magnetic ground state of Na$_2$PrO$_3$. $\mu$SR reveals
N\'eel antiferromagnetic order below $T_{\rm N}\! \sim\! 4.9$ K, with a small
static magnetic moment $m_{\rm static}\!\leq \! 0.22$~$\mu_{\rm B}/{\rm Pr}$
collinearly aligned along the $c-$axis. Inelastic neutron measurements reveal
the full spectrum of crystal field excitations and confirm that the Pr$^{4+}$
ground state wave function deviates significantly from the $\Gamma_7$ limit
relevant to the Kitaev model. Single and two magnon excitations are observed in
the ordered state below $T_N=4.6$ K and are well described by non-linear spin
wave theory from the N\'eel state using a magnetic Hamiltonian with Heisenberg
exchange $J=1$ meV and symmetric anisotropic exchange $\Gamma/J=0.1$,
corresponding to an XY model. Intense two magnon excitations are accounted for
by $g$-factor anisotropy $g_\mathrm{z}/g_\pm = 1.29$. A fluctuating moment
$\delta m^2 = 0.57(22)$ $\mu_{\rm B}^2/{\rm Pr}$ extracted from the energy and
momentum integrated inelastic neutron signal is reduced from expectations for a
local $J=1/2$ moment with average $g$-factor $g_{\rm avg}\approx 1.1$.
Together, the results demonstrate that the small moment in Na$_2$PrO$_3$ arises
from crystal field and covalency effects and that the material does not exhibit
significant quantum fluctuations..
