I watched Star Trek VI: The Undiscovered Country today, and once more I noticed that the first thing you see in the film is Sulu having a cup of tea. It got me thinking about cups and stuff in the TV series and in the films. So here's some of the more iconic ones..
"Tea. Earl Grey. Hot."
In Star Trek: The Next Generation, Captain Jean-Luc Picard uses this short glass teacup most of the time. It's a plain glass mug, with a black handle. This is actually a coffee mug made by Bodum. It comes in tall and short.
However, at other times, Picard uses a more elaborate, taller teacup. This is a Russian-style metal cup holder. It's modern in design, and not very elaborate (which is very unlike most Russian cup holders out there). The glass cup itself is nothing but a standard slender drinking cup.
Tea for two, Beverly?
In several episodes of Star Trek: The Next Generation, Picard uses a white porcelain tea set with pot. The cups slide into the side of the pot, to form a unit. This is a seven-piece porcelain tea set designed by Peter Saenger in the early 1970s. It's known as the "Design II Set". You can buy it from Saenger Porcelain for about $295.
"My first tour as captain of this vessel..."
In Star Trek VI: The Undiscovered Country, Captain Sulu has tea on the bridge just before the shock-wave from the collapse of Praxis (the Klingon moon) hits. This cup is a Pfaltzgraf porcelain cup and saucer. The design is known as the "Hampton Collection". You can also see the same design of porcelain used for cups, saucers, and plates used by the USS Enterprise crew during the dinner with the Klingons. To turn the Pfaltzgraf into Federation-ware, the production crew merely applied transparent decals.
For the scene in which Sulu's cup falls to the ground and shatters, you can see that the cup is a plain Pfaltzgraf, without any decals.
The Pfaltzgraf "Hampton" is available from Pfaltzgraf, or you can find used sets online. Pfaltzgraf even issued a series of Undiscovered Country porcelain with the USS Enterprise designs silk-screened onto the surface. You can still find originals of these online in places like eBay or Etsy, and replacement pieces are available from various stores, too.