There is no such thing as "starfleet marriage vows", as starfleet is a military/science organization which would mean they would have no need for something of that nature. Two starfleet officers could get married in a private ceremony or on the ship/facility they were currently serving on, but it assumed that the exact vows or ritual would be determined by cultural traditions. For example Betazoid traditon says that all the participants must be nude as in Will Riker's marriage to Counselor Troi on the Enterprise, where as Miles and Keiko O'Brien were completely clothed for their wedding.
During TOS, we only saw 1 wedding ceremony between officers, that of Robert Tomlinson & Angela Martine. You may click the hyperlinks for more information. TrekFan1984 Ends (talk) 15:00, May 18, 2014 (UTC)