I think you might be a bit confused about what the Meiji Restoration was. That is understandable, because the name "Meiji Restoration" can be misleading. The Meiji Restoration was not like the the Restoration of the English monarchy in 1660, where the monarchy was brought back into being after a period of rule by Parliament wherein the monarchy in exile. The Meiji Restoration did not involve a new emperor being chosen to literally restore the title, because there already was an emperor - the Emperor Meiji, or Mutsuhito to give his birth name. Mutsuhito became Emperor in February 1867 following the death of his father, the Emperor Kōmei.

The name "Restoration" reflects the fact that in November 1867, the last shogun, Tokugawa Yoshinobu, stepped down from that position and relinquished his prerogatives to the Imperial Court. In practice, the Yoshinobu sought to maintain de facto power, and was able to do so for a short while. However, in 1868 this came to an end as the Tokugawa forces were defeated in a series of battles by pro-Imperial armies, which mainly came from the Satsuma, Chōshū, and Tosa domains (leaders from these domains had been the main instigators in ending the shogunate). The "Restoration" therefore refers to the restoration of Imperial power in Japan, as opposed to the restoration of any actual individual. Had the Restoration not taken place, the Emperor Meiji still would have been on the throne, but his court would not have assumed the powers that it did with the end of the Tokugawa shogunate.

Today, the term Meiji Restoration is generally used as a catch-all term in order to describe the vast changes that took place in Japanese that began in 1867-68.