  In these proceedings we present preliminary results for the masses of the
proton, neutron and $\Omega^-$ baryons obtained from QCD+QED lattice
simulations performed with four dynamical quarks using C$^*$ boundary
conditions. These results are part of the ongoing effort of the RC${}^*$
collaboration discussed in the companion proceedings, and have been obtained on
a single ensemble in which the renormalised electromagnetic coupling is
$\alpha_{\text{em}}\sim 0.04$, the physical volume is $L\sim 1.7$ fm and the
masses of the four dynamical quarks have been tuned at the $U$--spin symmetric
point $m_d=m_s$. We demonstrate on this unphysical ensemble that baryon masses
can be calculated with satisfactory precision when including QED without the
need for gauge--fixing and perturbation theory. This makes us confident in the
effectiveness of the strategy presented here also in the case of simulations
closer to the physical point.
