  We describe pair-production models of spin-0 and spin-1/2 magnetic monopoles
and high-electric-charge objects in proton-proton and heavy-ion collisions,
considering both the Drell-Yan and the photon-fusion processes. In particular,
we extend the Drell-Yan production model of spin-1/2 high-electric-charge
objects to include $Z^0$-boson exchange for proton-proton collisions.
Furthermore, we explore spin-1/2 and, for the first time, spin-0 production in
ultraperipheral heavy-ion collisions. With matrix element calculations and
equivalent photon fluxes implemented in MadGraph5_aMC@NLO, we present
leading-order production cross sections of these mechanisms in $\sqrt{s} = 14$
TeV proton-proton collisions and $\sqrt{s_{\text{NN}}} = 5.5$ TeV
ultraperipheral lead-lead collisions at the LHC. While the mass range
accessible in ultraperipheral lead-lead collisions is much lower than that in
proton-proton collisions, we find that the theoretical production cross
sections are significantly enhanced in the former for masses below 82 GeV.
