Interestingly, in To Kill a Mockingbird each of the main characters experiences at least one incidence where their patience and/or courage will be directly tested. This is mainly because the topics of social equality and racial equality are so controversial and divisive that they actually uncover people for who they really are.
Boo Radley, the central tragic figure who looms in the background of the novel, is the most misunderstood of all characters. His most evident act of courage occurs in chapter 27 when he takes on Bob Ewell after the latter tries to come from behind Atticus's children as they walk home from a pageant, and tries to kill them.
We know that Jem is attacked first, then he warns Scout who runs, but she cannot get too far. There is a knife involved, and the assumption is that Boo got in between Scout and Ewell and stabbed Bob Ewell while defending the children. Heck Tate is convinced that this is what happened despite Atticus's assumption that it may have been Jem in self-defense. Tate went as far as stating why he is publicly defending Boo:
To my way of thinkin', Mr. Finch, taking the one man who's done you and this town a great service an' draggin' him . . . into the limelight . . . [is] a sin, and I'm not about to have it on my head
Either way, the official story was that Boo saved the kids (which he did) and that Ewell fell on his own knife.
Jem shows courage plenty of times in the story but the most memorable, aside from warning Scout about Ewell, is in chapter 15, when he faces head on the lynch mob organized by Walter Cunningham, Sr. When the group goes in to lynch Tom Robinson at the jail, Jem told his father that he refused to leave or take Scout home. One man even goes as far as touching Jem, but Scout --being smaller and quicker--kicked the man. Regardless of the fact that it was Scout that convinces the men to go away (by using her childlike charm to appeal to the human side of the men), Jem demonstrates that, like Atticus, he is not afraid to face the enemy. We also know that Atticus did appreciate Jem's efforts.
[Scout] assumed that Atticus was giving [Jem] hell for not going home, but I was wrong. As they passed under a streetlight, Atticus reached out and massaged Jem's hair, his one gesture of affection.
As far as Atticus, perhaps the moment where he teaches people about maturity and dignity is in the awful scene caused by Bob Ewell in chapter 22. As we know, Ewell was determined to insult and degrade Atticus however he could. Childish, immature and nasty as he is, he dares to insult and spit at Atticus at the post office:
Mr. Bob Ewell stopped Atticus on the post office corner, spat in his face, and told him he’d get him if it took the rest of his life.' [Miss Stephanie repeats Atticus' response] 'I wish Bob Ewell wouldn’t chew tobacco,' was all Atticus said about it.
Most importantly, Ewell continues to taunt Atticus and invites him for a fight. Atticus continues being the bigger person and not falling for Ewell's threats.
(Ewell) proud to fight, you n_g_er-lovin‘ b__tar_?' [...] 'No, too old,' put his hands in his pockets and strolled on..."
There you have how in the three instances the men had to face someone at least once during incidents that tested both their patience as well as their character.