Jem's courage is first challenged by Dill Harris regarding the Radley house:
"'You're scared,' Dill said, the first day. 'Ain't scared, just respectful,' Jem said. The next day Dill said, 'You're too scared even to put your big toe in the front yard'"(13).
Little did Jem know that he was going to be challenged to do more than just put his toe in the yard. Eventually Dill eggs him on enough that the following happened:
"Jem threw open the gate and sped to the side of the house, slapped it with his palm and ran back past us, not waiting to see if his foray was successful" (15).
The next summer after this first trial of manhood, the kids decide to roll Scout in a tire for fun. They misjudge their aim and she rolls right up to the front porch of the Radley house. Jem screams at Scout to bring back the tire, but she runs out of there without it. Dill reminds Jem that he had touched the house the previous summer, so it shouldn't be hard for him a year later.
"Jem looked at me furiously, could not decline, ran down the sidewalk, treaded water at the gate, then dashed in and retrieved the tire. 'See there?' Jem was scowling triumphantly. 'Nothin' to it'"(38).
Another frightful situation that Jem must use courage to endure is Mrs. Dubose. She is an old woman who is rumored to have a SCA pistol with her at all times--but that's not the half of it. She yells at the children as they pass her home and even calls Atticus some very bad names. Jem flips out and beats up her roses with Scout's baton. The consequence is he has to go over and read to the old woman every day until she says stop. Jem bravely goes over on the first day with Scout.
"'So you brought that dirty little sister of yours, did you?' was her greeting.
Jem said quietly, 'My sister ain't dirty and I ain't scared of you,' although I noticed his knees shaking"(106).
That was certainly a brave thing to say; and luckily, Mrs. Dubose doesn't scold him for it.
Jem's courage is ultimately tested far above and beyond running up to touch a person's house, or dealing with a grumpy old woman, when he stands up for his father in front of a lynch mob. Atticus tells Jem to go home two or three times and Jem doesn't move an inch, as follows:
"Jem shook his head. As Atticus's fists went to his hips, so did Jem's, and as they faced each other I could see little resemblance between them. . . Mutual defiance made them alike.
'Son, I said go home.'
Jem shook his head" (152).
Jem faces more intense situations as the story moves forward. First Jem faces the Radley house, then Mrs. Dubose, and then the lynch mob. By the end, Jem faces a few life-threatening situations. As Jem bravely conquers each challenge, he is ready for the next one and his courage stands ready to help him.