Panum began lecturing on music history in 1885, later arranging concerts at the end of her talks to present the music she had reviewed. In 1898, she was appointed as a teacher of theory and music history at Copenhagen's Glass Conservatory. In 1904, she lectured at the Folk University and from 1907 to 1931 she taught music history and musicology at the Royal Danish Academy of Music.[1]
In 1898, together with Louis Glass, she established the Music Education Association, which she managed from 1901 to 1903. Her writings included Nordeuropas gamle Strengeinstumenter (Northern Europe's Old Stringed Instruments, 1903), De folkelige Strengeinstrumenter i Nordens Middelalder (Popular Stringed Instruments in the North's Middle Ages, 1905).[2] Her most important work was Middelalderens Strengeinstrumenter og deres Forløbere i Oldtiden (1928), published in English in 1939 as The Stringed Instruments of the Middle Ages: Their Evolution and Development.[1]
In later life, she took a special interest in the old Norwegian instrument, the langeleik, which she tried to reintroduce in Denmark, persuading Carl Nielsen to compose a few pieces for the instrument. In 1930, she attempted unsuccessfully to promote further interest through a radio broadcast.[1]
Hortense Panum died in Copenhagen on 26 April 1933 and was buried in the Garrison Cemetery.[2][4]