An exhaust manifold is for an internal combustion engine on an outboard marine engine that is configured to power a propulsor to provide a thrust in a longitudinal direction. The exhaust manifold comprises an exhaust runner that transversely and longitudinally rearwardly conveys the exhaust gas from the internal combustion engine, an exhaust log that vertically upwardly conveys the exhaust gas from the exhaust runner, and an exhaust elbow that conveys the exhaust gas from the exhaust log vertically upwardly, longitudinally forwardly, and then vertically downwardly.