It can be argued that the Roman empire didn't truly end until WWI in 1918, 106 years ago.
The fall of the Byzantine Empire (aka the Eastern Roman Empire) resulted in a number of subdivided but diplomatically aligned states. By the end of the 19th century a number of European powers were still vying for some claim to the lineage of the Roman Empire (and the Emperor title). But as consequence of the war, the German/Prussian, Austro-Hungarian and Ottoman empires we're all dismantled (and France was out or the running because of the revolution) so every entity with a claim was dead or out of power for the first time since the 11th century.
The Byzantine Empire was the Eastern Roman empire - we really on refer to them differently for temporal convenience. The west were the Latin speakers and the east were the Greek speakers (as least for the first half-millennium). And many people still called themselves Emperor of Rome, in a continuous succession, after the fall of the west. For quite a while one of the Pope's titles was (legitimately) Emperor of the Holy Roman Empire.
By the 20th century it was down to 3 rightful heirs, all trying to make Europe recognize them as THE Emperor. But in the mean time their empires still recognized them as such.