In 2370, after the USS Hera was reported missing, the USS Excelsior and the Noble retraced the Hera's course for six days. The search failed at finding any evidence of the lost starship. (TNG: "Interface")
The Nobel fought in the Dominion War. In 2374, the starship reported numerous casualties to Starfleet Command. The name of the reporting ship and its registry and the casualties were named on the "Personnel Status Update" chart in the Deep Space 9 wardroom. (DS9: "In the Pale Moonlight" okudagram)
List of casualties
The Nobel was named for Alfred Nobel, a Swedish scientist and industrialist of the 19th century who invented dynamite and founded the famous Nobel Prize. (Star Trek Encyclopedia (4th ed., vol. 2, p. 85))
According to the Star Trek Encyclopedia, the USS Nobel was an Olympic-class hospital ship, and was the same ship as the USS Noble mentioned in "Interface". The scene in the script where the Nobel was mentioned was spelled "Noble", as before, the Encyclopedia mentioned this vessel as being one and the same as the Nobel, which was featured on a large computer display in some DS9 episodes.