His Imperial Majesty; Your Imperial Majesty
Honorific title used to refer to or address an emperor. The exact translation depends on context: 'His Imperial Majesty' when speaking about the emperor, 'Your Imperial Majesty' when addressing directly.
His Imperial Majesty graced the ceremony with his presence.
Your Imperial Majesty, I hope you are in good spirits.
Used specifically for the Emperor of Japan, while 皇帝陛下 is a more general term for emperors of other nations or historical contexts.
Compound of 皇帝 (emperor) and 陛下 (Your/His Majesty). The term is a standard honorific formation.