Anti-magnetic timepieces employ Mu metal shielding to redirect magnetic fields around, rather than through, the watch movement.

From the MuMetal Magnetic Shield Corp. FAQ:

MuMetal re-directs magnetic flux so it lessens the magnetic field’s influence on the item being shielded. Shielding does not eliminate or destroy magnetic fields, nothing does. It does, however, provide an easy path for the magnetic field to complete its path. You may think of it as a magnetic field conductor or shunt.

Hat tip Jack Forster.