Extremely strong magnetic fields change the vacuum index of refraction. This induces a lensing effect that is not unlike the lensing phenomenon in strong gravitational fields. The main difference between the two is the polarization dependence of the magnetic lensing, a behaviour that induces a handful of interesting effects. The main prediction is that the thermal emission of neutron stars with extremely strong magnetic fields is polarized - up to a few per cent for the largest fields known. This potentially allows a direct method for measuring their magnetic fields.