Would a starfaring society be as developed in other sciences as it is in energy generation and system engeneering? If true, is such society is as advanced in medicine/genetics/cybernetics as it is in space technology, it? It could have some very long-living beings, some kind of cyber-elves with lifespan around the dozens of millenia, due to their very advanced cybernetics, biochemistry and genetics. Then you combine that long lifespan with relativistic time dilatation and the cyber-elves could solve the time issues.
The second issue is the energy and resources spent on such travel. I have no idea of what could be worth the antimatter that will be spent during the travel but then, i'm not a cyber-elf. Maybe some very rare elements, like monopole magnets or other rare particles.