Emilia's courage comes out in the last scene. She calls Othello, who is of great social standing compared to her, a liar and a devil. To utter such words as a woman and one of a lower class would have been incredibly courageous in her day. She also turned on her husband in that scene in defense of Desdemona. She says that what Iago said of Desdemona cheating was false and she calls Iago a liar. She calls Othello an idiot for believing Iago. Unfortunately, Emilia's courage comes out a little too late. This is probably part of Shakespeare's purpose: waiting to tell the truth can cost lives.
Desdemona's courage is displayed throughout the play. She leaves her home and seeks relationship with Othello even though her father disapproves of their union. She confronts Othello with Cassio's requests, even though Othello doesn't want her to be a negotiator for others. Finally, when she knows he is about to kill her, she asks for a little more time and confesses her innocence. Some people would just cave and tell a murderous man what he wanted to hear, but Desdemona told him the truth. This was most certainly courageous because the result was death anyway.