An outboard engine assembly has an engine unit including an engine unit housing, an internal combustion engine disposed in the engine unit housing, the engine defining at least one combustion chamber, a gearcase connected to the engine unit housing, and an exhaust system, the exhaust system including an idle relief passage fluidly communicating with an exhaust passage, the idle relief passage having an idle relief outlet, the idle relief passage extending through the engine unit housing for supplying exhaust gases from the at least one combustion chamber to an exterior of the engine unit housing via the idle relief outlet, the idle relief outlet being disposed vertically higher than the exhaust outlet and vertically lower than a waterline when the outboard engine assembly is mounted to a watercraft and the watercraft is at rest, and a propulsion device operatively connected to the engine.