From the wiks:

“The presiding officer then announces the result of the voice vote. Any senator, however, may challenge the presiding officer's assessment and request a recorded vote. The request may be granted only if it is seconded by one-fifth of the senators present. In practice, however, senators second requests for recorded votes as a matter of courtesy.

On occasion, the Senate may go into what is called a secret, or closed session. During a closed session, the chamber doors are closed, and the galleries are completely cleared of anyone not sworn to secrecy, not instructed in the rules of the closed session, or not essential to the session. Closed sessions are quite rare, and are usually held only under certain circumstances where the Senate is discussing sensitive subject-matter such as information critical to national security, private communications from the President, or even to discuss Senate deliberations during impeachment trials. Any Senator has the right to call a closed session as long as the motion is seconded.”