Munch's scholarship included Norwegian archaeology, geography, ethnography, linguistics, and jurisprudence.

Munch's first great achievement, with Rudolph Keyser, was their three volumes of Norges Gamle Love (Norway's old laws), edited after a two-year research visit to Copenhagen.

In 1857, after producing numerous publications, he received a large grant for archives research in Rome and lived there from 1859 to 1861.

He took extensive notes from the volumes of papal letters, and sometimes drew accurate facsimiles of the texts.

He also edited Chronica regvm Manniae et insvlarvm: The chronicle of Man and the Sudreys (1874)[4] with Alexander Goss.