Quantum electrodynamics predicts that in a strong electric field, electron-positron pairs are produced by the Schwinger process, which can be interpreted as quantum tunnelling through the Coulomb potential barrier. If magnetic monopoles exist, monopole-antimonopole pairs would be similarly produced in strong magnetic fields by the electromagnetic dual of this process. The production rate can be computed using semiclassical techniques without using perturbation theory, and therefore it can be done reliably in spite of the monopoles' strong coupling to the electromagnetic field. I will explain this phenomenon and discuss the bounds on monopole masses arising from the strongest magnetic fields in the Universe, which are in neutron stars known as magnetars and in heavy ion collision experiments. In particular, I will discuss the lead-lead collisions carried out in the Large Hadron Collider at CERN in November 2018, and the open theoretical questions affecting the calculation.