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We report on a search for magnetic monopoles (MMs) produced in ultraperipheral Pb-Pb collisions during Run 1 of the LHC. The beam pipe surrounding the interaction region of the CMS experiment was exposed to $184.07\mathrm{\mu }{\mathrm{b}}^{-1}$of Pb-Pb collisions at 2.76 TeV center-of-mass energy per collision in December 2011, before being removed in 2013. It was scanned by the MoEDAL experiment using a SQUID magnetometer to search for trapped MMs. No MM signal was observed. The two distinctive features of this search are the use of a trapping volume very close to the collision point and ultrahigh magnetic fields generated during the heavy-ion run that could produce MMs via the Schwinger effect. These two advantages allowed setting the first reliable, world-leading mass limits on MMs with high magnetic charge. In particular, the established limits are the strongest available in the range between 2 and 45 Dirac units, excluding MMs with masses of up to 80 GeV at a 95% confidence level. Published by the American Physical Society2024