  We investigate the crystal structure, magnetic properties, and
crystalline-electric field of tetragonal, $I4_1/amd$, NaCeO$_2$. In this
compound, Ce$^{3+}$ ions form a tetragonally elongated diamond lattice coupled
by antiferromagnetic interactions ($\Theta_{CW} = -7.69$ K) that magnetically
order below $T_N = 3.18$ K. The Ce$^{3+}$ $J = 5/2$ crystalline-electric
field-split multiplet is studied via inelastic neutron scattering to
parameterize a $J_{eff} = 1/2$ ground state doublet comprised of states
possessing mixed $|m_z \rangle$ character. Neutron powder diffraction data
reveal the onset of $A$-type antiferromagnetism with $\mu=0.57(2)$ $\mu_B$
moments aligned along the $c$-axis. The magnetic structure is consistent with
the expectations of a frustrated Heisenberg $J_1$-$J_2$ model on the elongated
diamond lattice with effective exchange values $J_1 > 4 J_2$ and $J_1 > 0$.
