I don't think Arwen has the Resumé to re-forge the sword. But she could have gotten Elrond to do it. Elrond offered it in the Extended FoTR.
"I don't think Arwen has the Resumé to re-forge the sword." Me, either. But I'm sure she could find someone to do it for her. Anyway, it has to happen, and my idea is as good as any.