Officers recovered a number of items after searching a property in Jamaica Mews in the New Town area of Edinburgh yesterday.
Police said two small controlled explosions were carried out late last night at its Fettes headquarters and one this morning "for safety reasons".
A small number of residents were evacuated from the Jamaica Mews area while the search operation was going on yesterday as a precaution.
Police Scotland said a 38-year-old man has been arrested and charged with firearms offences.
The force added there was no danger to the public at any time.