  We simulate the passage through the Sun-Jupiter system of interstellar
objects (ISOs) similar to 1I/`Oumuamua or 2I/Borisov. Capture of such objects
is rare and overwhelmingly from low incoming speeds onto orbits akin to those
of known long-period comets. This suggests that some of these comets could be
of extra-solar origin, in particular inactive ones. Assuming ISOs follow the
local stellar velocity distribution, we infer a volume capture rate of
$0.051\,\mathrm{au}^3 \mathrm{yr}^{-1}$. Current estimates for orbital
lifetimes and space densities then imply steady-state captured populations of
$\sim10^2$ comets and $\sim10^5$ `Oumuamua-like rocks, of which 0.033% are
within 6au at any time.
