Congrats on the find, unfortunately, tungsten jewelry has no real value once sold. For me they are like mood rings.
I keep a few in my pouch that I throw back in surf when someone sees me recover a gold ring and argues it their ring even though they cant identity it. I look at the ring I just recovered and ask them what the engraving says and or what the gold K is. You can tell quickly if they are lying, if they correctly identify ring I return it, no problem.
I grab a tungsten ring or another junk ring from my pouch and toss it in surf telling them there go get it. Multiple times had someone try to claim a ring found, but was obvious they were lying.