May have some ideas, if my analysis is correct CERN have discovered sufficient anomalies in antimatter (specifically cold antihydrogen) to justify trying this experiment as in order for any weak antigravity to show up it has to only be near the centre of that chamber: too close to a wall and electrostatics takes over.
Additional data would be the mysterious belt of antimatter around Earth and also evidence of positrons in thunderstorms suggesting that we may have overlooked something. Ball lightning is also strange enough to justify further study.
In order to generate an antigravitational field it would have to trap the antimatter far enough from matter to offset its gravitational and electrostatic field(s).
In real terms this means beyond the point at which the mass is detectable using atomic clocks, so for a small 25g spacecraft that would be around 150 metres.
Charging up the spacecraft to a very high voltage may also assist with this and I've got some sketches here.
In fact this could by itself account for the strange distribution of energetic positrons in the Universe, if they are produced as a byproduct of frequent travel then we should be able to see "space lanes" around particularly popular star systems similar to contrails from aircraft by mapping out direction and energy of incident particles here on Earth using supercomputers to process this information with feedback from existing terrestrial planet finder tables.
The effect may indeed only work well with antihydrogen, the positrons are too hard for the drive to trap if freed from their host antiatoms so most simply get disposed of at the end of each trip and AP's recycled back into containment. This could lead to quite high energies in said positrons which we could also detect.
Making AP's is not "Simplez" but positrons are comparatively easy as decay products from a number of isotopes.