Emich was born at Osborne House, Isle of Wight, United Kingdom, the second child and only son of Ernst, Prince of Leiningen (1830–1904), (son of Karl, Prince of Leiningen and Countess Marie von Klebelsberg) and his wife, Princess Marie of Baden (1834–1899), (daughter of Leopold, Grand Duke of Baden and Princess Sophie of Sweden).

His paternal grandfather, Carl, 3rd Prince of Leiningen, was the half-brother of Queen Victoria.

He was baptised at Osborne House on 10 February 1866 and his godparents were his paternal great-aunt, Princess Feodora of Leiningen, his maternal uncle Frederick I, Grand Duke of Baden (represented by Hermann, Prince of Hohenlohe-Langenburg) and his paternal uncle Prince Eduard of Leiningen (represented by Ernest II, Duke of Saxe-Coburg and Gotha).

Emich married on 12 July 1894 in Langenburg his second cousin (both great-grandchildren of Princess Victoria of Saxe-Coburg-Saalfeld and her first husband Emich Karl, Prince of Leiningen), Princess Feodore of Hohenlohe-Langenburg (23 July 1866–1 November 1932), youngest child of Hermann, Prince of Hohenlohe-Langenburg and his wife, Princess Leopoldine of Baden.

They had five children: On the death of his father in 1904, Emich became the Prince of Leiningen.