The government lab for this is the Metals Assay Centre of the Ministry of Industry and Commerce (MOIC). It analyses precious metals and stamps hallmarks on them.
Where and when: Bahrain Financial Harbour, Seafront, second floor, Manama. Open Sunday to Thursday, 7:30 AM to 2:00 PM.
Contact: 80008001 or metalgem@moic.gov.bh.
Fees: MOIC publishes a separate fee sheet, "Fees of Precious Metals Analysis and Hallmarking", plus the terms for hallmarked items and the documents to bring, on its Service Centers page. Check it before you go, since prices depend on the test.