  The discoveries of two Interstellar Objects (ISOs) in recent years has
generated significant interest in constraining their physical properties and
the mechanisms behind their formation. However, their ephemeral passages
through our Solar System permitted only incomplete characterization. We
investigate avenues for identifying craters that may have been produced by ISOs
impacting terrestrial Solar System bodies, with particular attention towards
the Moon. A distinctive feature of ISOs is their relatively high encounter
velocity compared to asteroids and comets. Local stellar kinematics indicate
that terrestrial Solar System bodies should have experienced of order unity ISO
impacts exceeding 100 km/s. By running hydrodynamical simulations for
projectiles of different masses and impact velocities, up to 100 km/s, we show
how late-stage equivalence dictates that transient crater dimensions are alone
insufficient for inferring the projectile's velocity. On the other hand, the
melt volume within craters of a fixed diameter may be a potential route for
identifying ISO craters, as faster impacts produce more melt. This method
requires that the melt volume scales with the energy of the projectile, while
crater diameter scales with the point-source limit (sub-energy). Given that
there are probably only a few ISO craters in the Solar System at best, and that
transient crater dimensions are not a distinguishing feature for impact
velocities at least up to 100 km/s, identification of an ISO crater proves a
challenging task. Melt volume and high-pressure petrology may be diagnostic
features once large volumes of material can be analyzed in situ.
