Picard used to drink out of a very novel-looking tea cup. It wasn't china, it was made of glass and had a sort of black-wire handle that gripped the cup, just under the lip. I found out, too late, that there was an entire set to this that you could buy - and wanted it badly.
Keep your eyes on eBay.
The set designers and prop finders of all the Treks used to scour retail stores and catalogs looking for "cool stuff" that would pass for 23rd/24th century items. Remember McCoy's TOS scalpels were all unusual salt and pepper shakers they had already amassed when the script required one futuristic salt shaker prop on set for "The Man Trap".
That TNG tea set would have been a commercially available product. I recall them. I think my local Target sold them. But not a Star Trek collectible until it was featured on the show.
There was also an expensive commercial chess-like board game using black and white spheres that was featured in Ten Forward and later sold with "as seen on TNG". Ah, it was called "Terrace":
http://holodeck3.wordpress.com/2012/07/30/games-in-star-trek/