I feel sure I've read something more in depth regarding the gem, either from CT or from unpublished writings. I can't think of anything specific, though.
My thought therefore would be that the jewel had more of a symbolic purpose than one of actual power. Arwen's words to Frodo upon giving to him were:
Quote:
'If your hurts grieve you still and the memory of your burden is heavy, then you may pass into the West, until all your wounds and weariness are healed. But wear this now in memory of Elfstone and Evenstar with whom your life has been woven!'
And she took a white gem like a star....and she set the chain about Frodo's neck.'When the memory of the fear and the darkness troubles you,' she said, 'this will bring you aid.'
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ROTK Many Partings
Perhaps the gem was first, a token that Frodo was allowed to take Arwen's place aboard ship with Elrond. But before that could occur, if Frodo felt too oppressed by his memories and experiences, the gem was a symbol of hope for the future: a reminder that there was a place he could go, and be at peace.