  Accurate measurements of the masses of neutron stars are necessary to test
binary evolution models, and to constrain the neutron star equation of state.
In pulsar binaries with no measurable post-Keplerian parameters, this requires
an accurate estimate of the binary system's inclination and the radial velocity
of the companion star by other means than pulsar timing. In this paper, we
present the results of a new method for measuring this radial velocity using
the binary synthesis code Icarus. This method relies on constructing a model
spectrum of a tidally distorted, irradiated star as viewed for a given binary
configuration. This method is applied to optical spectra of the newly
discovered black widow PSR J1555-2908. By modelling the optical spectroscopy
alongside optical photometry, we find that the radial velocity of the companion
star is $397\pm4$ km s$^{-1}$ (errors quoted at 95\% confidence interval), as
well as a binary inclination of $>75^{\rm o}$. Combined with $\gamma$-ray
pulsation timing information, this gives a neutron star mass of
1.67$^{+0.15}_{-0.09}$ M$_\odot$ and a companion mass of
0.060$^{+0.005}_{-0.003}$ M$_\odot$, placing PSR J1555-2908 at the observed
upper limit of what is considered a black widow system.
