Elizabeth is a strong character whose strengths are perhaps not too apparent at first. Initially she appears as little more than a once-betrayed and now perpetually-suspicious wife, questioning her husband's every move. She also forms a contrast with the fiery, feisty Abigail in that she is dutiful, morally scrupulous, and maybe, just a little dull.
Elizabeth grows in stature as the play wears on, however. She shows a considerable measure of courage when she is arrested by the court; in her own quiet way she faces up to its inquisition. She also proves her loyalty to Proctor, telling a lie to try and protect him, although this sadly makes things worse for him.
It is only in Act IV, though, that we really see her depth of character, in her private poignant moments with her husband in prison. She confesses her own sense of inadequacy which she believes drove him to adultery: 'It takes a cold wife to prompt lechery.' This shows that that she does not just blame him for their marriage going wrong as she seemed to do earlier - she is also capable of self-criticism. Her loyalty and real love for him are nowhere more evident than in this scene. She wants his life to be spared but she understands why he feels he cannot tell a lie to save himself.
Finally, just before Proctor is about to be hanged, Elizabeth gives way to emotion and rushes to him, while he 'kisses her with great passion'. At this climactical moment of the play, they are as one, united both in love and in defiance of the court. Elizabeth shows tremendous integrity, bravery and loyalty over the course of the play.
Here is a video analyzing the characters of the play: