Are there any families still today that are descendants of Roman emperors?
Unfortunately, records of Roman Imperial families and post-empirical Europe are extremely scant and it is difficult to exactly discern where many royal family trees began. It is true that almost every royal family in Europe can trace their ancestry back to Charlemagne, but this only stretches back to the 8th and 9th century BC.
The turbulent nature of Europe in the 5th to 8th century means that the transitional period of the Roman Empire to the Medieval Period is a difficult era to study. In short, there is no family which can fully trace their lineage back to a Roman Emperor, but many can be traced to Charlemagne. If a link from Charlemagne to a Roman Emperor was ever found, then it could be verified who were the true descendants of the Roman Emperors, but this is extremely unlikely.