Sweet and Elite (S2)
Even though this is more about Rarity, I still consider this to be a Rarity and Twilight episode. One big reason is that it involves Twilight’s birthday and Rarity wanting to make a new dress for her. But spending time with Canterlot’s elite cuts into dress-making time that the dress ended up being simple and plain. Plus, with Rarity jumping between Twilight’s party indoors and the Elite party outdoors, Rarity was worried about letting Twilight down. In the end, Rarity announces to the Canterlot Elite of VIPS that she does come from a simple town like Ponyville and got the approval of one of Canterlot’s most influential unicorns, Fancy Pants. Until a better, more focused episode comes, Sweet and Elite is the episode that makes me think of Twilight and Rarity together.
Other Nominees: None others

Putting Your Hoof Down (S2) Unofficially challenged for position by a Season 6 episode.
This episode isn’t bolded because since I can’t find an episode that focuses on these two ponies specifically, I’m settling for an episode where we see the most screen time with these two together. As of the end of Season 5, Pinkie Pie and Rarity had spent the most time together in this episode as the Straight Mares to Fluttershy’s conflict. They both give Fluttershy methods of being less of a doormat, witness the change in Fluttershy’s behavior at Sugarcube Corner, got chewed out by “New” Fluttershy, and are present to Iron Will’s “collect payment” scene where Fluttershy realizes she’s not 100% satisfied with her new self that she refused to pay, leaving Iron Will to learn a new method: “No means No”. Whew! However…before I was able to post this, an early episode from Season 6 aired, and it has Rarity and Pinkie more closely to a starring role. By this point, I’m not “officially” including Season 6 episodes, so I’ll leave this post like this for now.
Other Nominees: None others

Sonic Rainboom (S1)/ Rarity Investigates (S5)
For a long time, Sonic Rainboom was the episode that first comes to my mind when I think of an episode focusing on Rarity and Rainbow Dash. In SR, Rainbow may have been the main character to compete in the Young Flyers competition. But remember: it was Rarity who knew Rainbow was feeling really nervous, so Rare got Twilight to find a spell to allow non-Pegasi ponies to go up to Cloudsdale. Short version: Rare becomes uncharacteristically egotistical with new Butterfly wings and ends up joining the completion too, which just makes Rainbow more nervous. In the end, Rarity nearly dies, but it leads to Rainbow performing the 2nd Sonic Rainboom of her life and saving Rarity’s life. Rarity learns the lesson about “keeping her hooves on the ground and being there for her friends.” But now, with Rairty Investigates, Rarity returns the favor to Rainbow by proving her innocence and saving Rainbow’s reputation with the Wonderbolts. The latter episode clearly is the better one by having Rarity completely on Rainbow’s side as opposed to making the situation worse for the Pegasus.
Other Nominees: None others.

Look Before You Sleep (S1)/ Made in Manehatten (S5)
For a brief moment I’d consider replacing Look Before You Sleep with the more recent Made in Manehatten. But looking back, LBYS was a bottle episode, having just Applejack, Rarity and Twilight in a single location. Because of the small cast, A.J. and Rare have much more contrasting interactions with each other here than in their Map episode, Made in Manehatten. So, I’ve decided to let LBYS keep its title of “A.J and Rare”
Other Nominees: Simple Ways (S4), Trade Ya (S4)

Green Isn’t Your Color (S1)
This episode is the one most focused on Rarity and Fluttershy. Rarity gets jealous when Fluttershy gets a modeling job instead of her, though Rarity tries to support her by insisting Fluttershy does the job. Fluttershy actually hates being a model, but continues to do it because of Rarity’s insisting. Both confine in Twilight how they really feel, but eventually admit their feelings about it to each other. So yeah, these two Beauties of the Mane 6 have this episode as “their” episode.
Other Nominees: Putting Your Hoof Down (S2), Castle-Mania (S4), Filli Vanilli (S4),