Ørsted was elected a Fellow of the Royal Society of Edinburgh in March 1821, a Foreign Member of the Royal Society of London in April 1821, a foreign member of the Royal Swedish Academy of Sciences in 1822, a member of the American Philosophical Society in 1829, and a Foreign Honorary Member of the American Academy of Arts and Sciences in 1849.
He founded the  (Society for the Dissemination of Natural Science, SNU) in 1824. He was also the founder of predecessor organizations which eventually became the Danish Meteorological Institute and the Danish Patent and Trademark Office. In 1829, Ørsted founded  (College of Advanced Technology), which was later renamed the Technical University of Denmark (DTU).
In 1824, Ørsted made a significant contribution to chemistry by being the first person to successfully produce aluminium in its metallic state, albeit in a less-than-pure form. In 1808, Humphry Davy had predicted the existence of the metal which he gave the name of alumium. However his attempts to isolate it using electrolysis processes were unsuccessful; the closest he came was an aluminium-iron alloy. Ørsted succeeded in isolating the metallic form by reacting aluminium chloride with potassium amalgam (an alloy of potassium and mercury) and then boiling away the mercury, which left small "chunks" of metal that he described as appearing similar to tin. He presented his results and a sample of the metal at meetings of the Danish Academy of Sciences in early 1825, but otherwise appears to have considered his discovery to be of limited importance. This ambivalence, coupled with the limited audience for the Danish Academy's journal in which the results had been published, meant that the discovery went mostly unnoticed by the wider scientific community at the time. Busy with other work, in 1827 Ørsted gave his friend, the German chemist Friedrich Wöhler, permission to take over the research. Wöhler was able to produce approximately  of aluminium powder soon thereafter, using a process of his own design, before finally, in 1845, isolating a quantity of solid metal sufficient for him to describe some of its physical properties.
Ørsted died in Copenhagen in 1851, aged 73, and was buried in the Assistens Cemetery.