  The MUSE experiment at the Paul Scherrer Institute is measuring elastic
lepton-proton scattering cross sections in a four-momentum transfer range from
$Q^2$ of approximately 0.002 to 0.08 GeV$^2$ using positively and negatively
charged electrons and muons. The extraction of the Born cross sections from the
experimental data requires radiative corrections. Estimates of the instrumental
uncertainties in those corrections have been made using the ESEPP event
generator. The results depend in particular on the minimum lepton momentum that
contributes to the experimental cross section and the fraction of events with
hard initial-state radiation that is detected in the MUSE calorimeter and is
excluded from the data. These results show that the angular-dependent
instrumental uncertainties in radiative corrections to the electron cross
section are better than 0.4 % and are negligible for the muon cross section.
