Seven years ago, Shadrach Mugoya Levi drove three hours from his rural village of Magada in the Namutumba District of Uganda to find a woman named Naomi. His friends had insisted he meet her. When he arrived at her house, her mother answered the door and said: “No, my daughter is too young.”

“At first I feared him,” said Naomi Namusoosa of that introduction. She was 16 at the time, and he was 21.

Mr. Levi, an orphan who helped raise himself and two of his younger siblings up from poverty, was looking for a wife. “A good woman, someone who will be so nice to me, a good listener, and a cook who will not give me a hard time,” he said.