Perhaps by patiently waiting for Aragorn to 'earn the sceptre', she shows her faith in him being able to fulfill his fate. (
Estel is Hope in the sense of Faith or Trust. For more on that see
Hope and Hopelessness.) The Standard she made for him is evidence of this
estel. Her faith may be a greater support to him than going with him as a helpmate. Besides, while she is in Rivendell, he need not worry about her safety while he fights the War of the Ring; he can concentrate on his task.
Further, by 'staying home' she negates the possiblity of Elrond claiming that Aragorn did not earn his crown because Arwen helped him - he didn't do it on his own. (Not that I know how she could have helped by going with him.)
[ November 28, 2002: Message edited by: Lostgaeriel ]