Maxwell married Katherine Mary Dewar, the daughter of the Principal of Marischal College, Aberdeen. Katherine became his close companion and assistant, helping him with his experiments and providing him with unwavering support throughout his life.

Maxwell and Katherine lived in London during his professorship at King's College and later moved to Cambridge when he became the director of the Cavendish Laboratory. They remained childless, and Katherine took care of Maxwell's aunt, Jane Cay, who lived with them for many years. Maxwell was known for his kindness, generosity, and strong religious beliefs.

Maxwell died of abdominal cancer at the age of 48 in Cambridge. He was buried in Parton Kirk, near Glenlair, his family estate. His early death was a great loss to the scientific community, cutting short a brilliant career and leaving many unanswered questions in physics.