The observability of old isolated compact remnants (ICoRs) is one of the open issues in the astrophysics of compact objects. To date, blind searches for neutron stars and stellar-mass black holes likely accreting from the interstellar medium have failed to reveal any good candidates. Following the results of recent simulations of compact object kinematics in the Galactic potential, we perform a quantitative analisys of the expected contribution of ICoRs to the microlensing event rate towards the bulge. Our results suggest that microlensing observations can be a powerful tool to probe the statistical properties of ICoRs. Also, follow-up observations of microlensing events with favourable parameters may allow the direct detection of the long sought-after old isolated compact remnants.