Under what circumstance do you wear the NCO Saber?

SGT (Join to see), the Army NCO sword is straight and has the white handle and the other is the Army officer saber. Both are available from Marlow White.
MSG (Join to see) CW3 (Join to see) SGM Jeff Mccloud

Officer saber
NCO sword
Can be used in any ceremony, see appendix F of TC 3-21.5.

The only time I've seen an NCO wear the saber was for a wedding. And they wore the cap and gloves. Otherwise, there really is no call for us to wear it.

First, NCOs (unless for uniformity purposes at a special event like a wedding), don't have sabers, they have swords. Officers have sabers. Second, to answer your question, it all depends. As I said, special events such as weddings are the most common, however, there are a few other events as well, but they are all ceremonious. Additionally, color guard may also wear a sword a saber at specific events.

The Cavalry is the only branch where it's NCO's are authorized to carry a saber. In all other instances it is a sword. And then, usually at the CO's discretion during formal military functions or in drill. It is not considered a normal appurtennance for the ASU or Mess Dress unless, as previouosly stipulated, you are ordered to wear it by your commanding officer.
It's a different story in the Cav. But I'd be telling tales if I went down that path.