  We present the cross sections for both electromagnetic and diffractive
dissociation of protons for semiexclusive production of $J/\psi$ mesons in
proton-proton collisions at the LHC. Differential distributions in missing mass
($M_X$), as well as distributions in rapidity and transverse momentum of the
$J/\psi$ are calculated for $\sqrt{s} = 7$ TeV and 13 TeV proton proton
collisions. We compare the distributions for purely electromagnetic and purely
diffractive proton excitations/dissociation. We predict cross sections for
electromagnetic and diffractive excitations of similar order of magnitude.
