  We determine the light meson spectrum in QCD in the presence of background
magnetic fields using quenched Wilson fermions. Our continuum extrapolated
results indicate a monotonous reduction of the connected neutral pion mass as
the magnetic field grows. The vector meson mass is found to remain nonzero, a
finding relevant for the conjectured $\rho$-meson condensation at strong
magnetic fields. The continuum extrapolation was facilitated by adding a novel
magnetic field-dependent improvement term to the additive quark mass
renormalization. Without this term, sizable lattice artifacts that would
deceptively indicate an unphysical rise of the connected neutral pion mass for
strong magnetic fields are present. We also investigate the impact of these
lattice artifacts on further observables like magnetic polarizabilities and
discuss the magnetic field-induced mixing between $\rho$-mesons and pions. We
also derive Ward-Takashi identities for QCD+QED both in the continuum
formulation and for (order $a$-improved) Wilson fermions.
