Examine the scepter to obtain the Red Jewel. This goes into the Bejeweled Box, which you can get in the Interrogation Room. Accessing this area requires the Club Key, so if you don't have that yet, keep progressing the story until you get it. Once you've got the Bejeweled Box, combine it with the Red Jewel to get the S.T.A.R.S. badge. You can use this item in two locations: the Underground Stairs in the Middle section of the Underground Facility, and the S.T.A.R.S. Office.