Emperor
The first Austrian Emperor was the last Holy Roman Emperor Francis II. In the face of aggressions by Napoleon, Francis feared for the future of the Holy Roman Empire. He wished to maintain his and his family's Imperial status in the event that the Holy Roman Empire should be dissolved, as it indeed was in 1806 when an Austrian-led army suffered a humiliating defeat at the Battle of Austerlitz. After which, the victorious Napoleon proceeded to dismantle the old "Reich" by severing a good portion from the empire and turning it into a separate Confederation of the Rhine. With the size of his imperial realm significantly reduced, Francis II, "Holy Roman Emperor" became Francis I, "Emperor of Austria". The new imperial title may have sounded less prestigious than the old one, but Francis' dynasty continued to rule from Austria and a Habsburg monarch was still an emperor ("Kaiser"), and not just merely a king ("König"), in name.
Constantine VI
Constantine VI was the final ruler to be universally recognized as Roman Emperor, being recognized as such by both the Empire which he ruled in the east, the papacy and the Western European powers over which the pope held suzerainty. With his mother becoming Empress regnant upon his deposition, the papacy crowned Charlemagne as a new Emperor in Western Europe, asserting that a woman could not be Empress in her own right. This laid the foundations of a new polity, independent of the East, that would evolve into the "Holy Roman Empire".