  The superconductivity in the rare-earth transition metal ternary borides
$R$RuB$_2$ (where $R$ = Lu and Y) has been investigated using muon-spin
rotation and relaxation. Measurements made in zero-field suggest that
time-reversal symmetry is preserved upon entering the superconducting state in
both materials; a small difference in depolarization is observed above and
below the superconducting transition in both compounds, however this has been
attributed to quasistatic magnetic fluctuations. Transverse-field measurements
of the flux-line lattice indicate that the superconductivity in both materials
is fully gapped, with a conventional s-wave pairing symmetry and BCS-like
magnitudes for the zero-temperature gap energies. The electronic properties of
the charge carriers in the superconducting state have been calculated, with
effective masses $m^*/ m_\mathrm{e} = $ $9.8\pm0.1$ and $15.0\pm0.1$ in the Lu
and Y compounds, respectively, with superconducting carrier densities
$n_\mathrm{s} = $ ($2.73\pm0.04$) $\times 10^{28}$ m$^{-3}$ and ($2.17\pm0.02$)
$\times 10^{28}$ m$^{-3}$. The materials have been classified according to the
Uemura scheme for superconductivity, with values for
$T_\mathrm{c}/T_\mathrm{F}$ of $1/(414\pm6)$ and $1/(304\pm3)$, implying that
the superconductivity may not be entirely conventional in nature.
