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.
Roman emperor
Due to the cultural rupture of the Turkish conquest, most western historians treat Constantine XI as the last meaningful claimant to the title Roman Emperor. From 1453, one of the titles used by the Ottoman Sultans was "Caesar of Rome" (Turkish: "Kayser-i Rum"), part of their titles until the Ottoman Empire ended in 1922. A Byzantine group of claimant Roman emperors existed in the Empire of Trebizond until its conquest by the Ottomans in 1461, though they had used a modified title since 1282.