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.
Romulus Augustulus
Some sources suggest that Julius Nepos claimed to hold legally the title of emperor when Odoacer took power. However, few of Nepos' contemporaries were willing to support his cause after he fled to Dalmatia. Some historians regard Julius Nepos, who ruled in Dalmatia until being murdered in 480, as the last lawful Western Roman Emperor.