The only phenomenon we know about that kind of resembles "negative mass" is the outward pushing force that is created from bringing conductive plates together via the Casimir effect. Could you potentially create a similar force by carefully shaping an controlling tined magnetic fields that "compress" each other in a fashion that leads to a similar effect? IF you used very intense fields created by superconducting magnets, could you perhaps use this to distort space enough to decouple an object from inertia and perhaps move at very high speeds?