We investigate properties of Galactic microlensing events in which a stellar object is lensed by a neutron star. For an all-sky photometric microlensing survey, we determine the number of lensing events caused by $∼10^{5}$ potentially-observable radio pulsars to be $∼0.2\ \rm{yr^{-1}}$ for $10^{10}$ background stellar sources. We expect a few detectable events per year for the same number of background sources from an astrometric microlensing survey. We show that such a study could lead to precise measurements of radio pulsar masses. For instance, if a pulsar distance could be constrained through radio observations, then its mass would be determined with a precision of $∼10\%$. We also investigate the time-scale distributions for neutron star events, finding that they are much shorter than had been previously thought. For photometric events towards the Galactic centre that last $∼15$ days, around $7\%$ will have a neutron star lens. This fraction drops rapidly for longer time-scales. Away from the bulge region we find that neutron stars will contribute $∼40\%$ of the events that last less than $∼10$ days. These results are in contrast to earlier work which found that the maximum fraction of neutron star events would occur on time-scales of hundreds of days. ; Comment: 10 pages, accepted for publication in ApJ. v2 updated to reflect change of title in proof stage