Officers recovered a number of items after searching a property in Jamaica Mews in the New Town area of Edinburgh on Wednesday.
Police said two small controlled explosions were carried out on Wednesday night at its Fettes headquarters and one yesterday morning "for safety reasons".
A number of residents were evacuated from the Jamaica Mews area as a precaution while the search operation was going on.
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.