The promise

"The Valar indeed may not withdraw the gift of death, which comes to Men from Ilúvatar, but in the matter of the Half-elven Ilúvatar gave to them the judgement; and they judged that to the sons of Eärendil should be given choice of their own destiny. And Elrond chose to remain with the Firstborn, and to him the life of the Firstborn was granted. But to Elros, who chose to be a king of Men, still a great span of years was allotted, many times that of the Men of Middle-earth; and all his line, the kings and lords of the royal house, had long life even according to the measure of the Númenóreans. But Elros lived five hundred years, and ruled the Númenóreans four hundred years and ten." (J.R.R. Tolkien "The Silmarillion")
It is a drawing to the fan fiction story abut the last meeting of Elrond and Elros. It's on the site of the Hungarian Tolkien Society: [link]
" 'I will take care of them' turn Elrond suddenly to his brother, read his thoughts 'Take care of your descendants, as if you were next to ...' "