With a private commissioned portrait, there's yourself, the sitter, and sometimes the sitter's family, who typically pays for it.
(Video link) With a portrait of an important public figure such as Kate, Duchess of Cambridge, there's yourself, the sitter, the Royal Family, the public, the pundits, and your fellow painters. That's a lot of people to think about. And which face do you try to capture, the "natural self" or the "official self"?
Artist Paul Emsley says that "after initially feeling that it was going to be an unsmiling portrait, I think actually that it was the right choice in the end to have her smiling, because that's really who she is, I think." After two sessions, he worked from a photo that he and Kate both approved (below, thanks, Mark Heng)
In the portrait, Kate has a complex expression called a "stifled smile." The smile is restrained by the action of the orbicularis oris, mentalis, and triangularis muscles. Those muscles act together to oppose the normal smiling action of the zygomaticus major.
Try to match the expression yourself, and you can feel the conflicting tensions.
In his book about facial expressions, Gary Faigin says that in the stifled smile, "the lips are frozen in a middle position and surrounded by a complex muscular landscape."
The stifled smile can appear either shy, endearing, smirking, impish, conflicted, scheming, self-conscious, or self-satisfied. Faigin says it's often used in advertising, but rarely in art.
Edit: Poll results from 78 votes "What emotion does Kate's portrait suggest?": Smirking 24 votes, Conflicted 15, Self conscious 14, Endearing 13, Self satisfied (tie) 13, Impish 9, Other 9 (tie), Shy 5, Scheming 4 votes.
What emotion does Kate's expression suggest to you? And does it matter what you or I think? Both the artist and the model are reportedly happy with the results. According to Marvin Mattelson, quoted in the video piece, that's all that really matters. If anyone else likes it, that's just a bonus.
Book: The Artist's Complete Guide to Facial Expression
Photo of artist is from MSN News
Huffington Post: "Kate Middleton Portrait Unveiled....And It's Awkward." (1400+ comments)
Making a Mark blog, with two additional videos
Paul Emsley's website