För att han egentligen inte träffade Nazgûl:
'Look!' he [Strider] cried; and stooping he lifted from the ground a black cloak that had lain there hidden by the darkness. A foot above the lower hem there was a slash. 'This was the stroke of Frodo's sword,' he said. 'The only hurt that it did to his enemy, I fear; for it is unharmed, but all blades perish that pierce that dreadful King.'
Så Frodo slog häxkungens kappa, men slog inte något annat.