  We report the findings of our extensive study of the spectra of flavoured
mesons in lattice gauge theories with symplectic gauge group and fermion matter
content treated in the quenched approximation. For the $Sp(4)$, $Sp(6)$, and
$Sp(8)$ gauge groups, the (Dirac) fermions transform in either the fundamental,
or the 2-index, antisymmetric or symmetric, representations. This study sets
the stage for future precision calculations with dynamical fermions in the low
mass region of lattice parameter space. Our results have potential
phenomenological applications ranging from composite Higgs models, to top
(partial) compositeness, to dark matter models with composite, strong-coupling
dynamical origin. Having adopted the Wilson flow as a scale-setting procedure,
we apply Wilson chiral perturbation theory to extract the continuum and
massless limits for the observables of interest. The resulting measurements are
used to perform a simplified extrapolation to the large-$N$ limit, hence
drawing a preliminary connection with gauge theories with unitary groups. We
conclude with a brief discussion of the Weinberg sum rules.
