  We investigate the magnetic ground state of Sm$_3$BWO$_9$ with the distorted
kagome lattice. A magnetic phase transition is identified at $T_N=0.75$ K from
the temperature dependence of specific heat. From $^{11}$B nuclear magnetic
resonance (NMR) measurements, an incommensurate magnetic order is shown by the
double-horn type spectra under a $c$-axis magnetic field. While, absence of
line splitting is observed for field oriented within the $ab$-plane, indicating
the incommensurate modulation of the internal field strictly along $c$-axis.
From the spin dynamics, the critical slowing down behavior is observed in the
temperature dependence of $1/T_1$ with $\mu_0H\perp c$-axis, which is
completely absent in that with $\mu_0H||c$-axis. Based on the local symmetry of
$^{11}$B sites, we analyze the hyperfine coupling tensors and propose two
constraints on the possible magnetic structure. The single ion anisotropy
should play an important role in the determination of the contrasting ground
states of Sm$_3$BWO$_9$ and Pr$_3$BWO$_9$.
