  We report muon spin relaxation ($\mu$SR) and magnetization measurements,
together with synthesis and characterization, of the Li-intercalated layered
superconductors Li$_{x}$HfNCl and Li$_{x}$ZrNCl with/without co-intercalation
of THF (tetrahydrofuran) or PC (propylene carbonate). The 3-dimensional (3-d)
superfluid density $n_{s}/m^{*}$ (superconducting carrier density / effective
mass), as well as the two dimensional superfluid density $n_{s2d}/m^{*}_{ab}$
(2-dimensional (2-d) area density of superconducting carriers / ab-plane
effective mass), have been derived from the $\mu$SR results of the
magnetic-field penetration depth $\lambda_{ab}$ observed with external magnetic
field applied perpendicular to the 2-d honeycomb layer of HfN / ZrN. In a plot
of $T_{c}$ versus $n_{s2d}/m^{*}_{ab}$, most of the results lie close to the
linear relationship found for underdoped high-$T_{c}$ cuprate (HTSC) and
layered organic BEDT superconductors. In Li$_{x}$ZrNCl without THF
intercalation, the superfluid density and $T_{c}$ for $x$ = 0.17 and 0.4 do not
show much difference, reminiscent of $\mu$SR results for some overdoped HTSC
systems. Together with the absence of dependence of $T_{c}$ on average
interlayer distance among ZrN / HfN layers, these results suggest that the 2-d
superfluid density $n_{s2d}/m^{*}_{ab}$ is a dominant determining factor for
$T_{c}$ in the intercalated nitride-chloride systems. We also report $\mu$SR
and magnetization results on depinning of flux vortices, and the magnetization
results for the upper critical field $H_{c2}$ and the penetration depth
$\lambda$. Reasonable agreement was obtained between $\mu$SR and magnetization
estimates of $\lambda$. We discuss the two dimensional nature of
superconductivity in the nitride-chloride systems based on these results.
