We describe pair-production models of spin-0 and spin-½ magnetic monopoles and high-electriccharge 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-½ highelectric-charge objects to include Z 0 -boson exchange for proton-proton collisions. Furthermore, we explore spin-½ 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 √ s = 14 TeV protonproton collisions and √ sNN = 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.