I don't remember details anymore, but there were some observations that some (deep space) astronomical object somewhere was accelerating and there were no models at the time that would explain that. I tried to explain it by a magnetic dipole in an non-homogeneous interstellar magnetic field.
If you know the gradients and the dipole moment you can calculate the force on the dipole.
I think it required a magnetar-level dipole to get some non-trivial forces out of the interstellar field. Anyway, I don't know if that theory ever got anywhere. Probably not. I never got any calls back from the people I presented that work to.
A spaceship would have a much lower mass than a star or whatever I was calculating that for, so I guess the requirements would be lower. Still, my gut feeling would be a magnet much beyond what you can do with today's superconductors. It would also only allow a one-way travel along the local field gradient. No round trips.
So slightly more imaginable than the Alcubierre drive in that it does not break known laws of physics or require vast quantities of unobtainium (negative mass, lots of antimatter, etc.), but completely impractical with current or foreseeable technology. Might also be fundamentally impractical since the energy/mass requirements to generate a field powerful enough to overcome gravity and other forces acting on the spacecraft might be too large... the thrust/weight ratio math might not work even for micro-gravitational fields.
Turn the magnet around?
(note) and it must not be permanent magnet, as the sibling explains - you must vary the magnetic field to "convert it" into electric field which then does the lift
On the other hand, some magnetic fields (not all) can be transformed into electric fields by a change of reference frame. In that case, the electric field can be used to do work. But I don't believe that's possible on these scales.
edit: For magnetism I believe the force comes from virtual photons maybe electrostatic is on a different scale, either bigger or smaller.
everybody on 4chan /sci was talking about this a few weeks ago. seems like you can get incredible thrust from solar wind that increases proportionally with radius from the sun for constant acceleration, all with a small standard electric motor. upon cursory investigation by me it seems sorta legit. needs testing beyond earth orbit but ground tests are reported to be successful.