When Pablo Picasso was told that the 1905-06 portrait he painted of Gertrude Stein didn't look like her, his response was, "It will." By that he meant that long after the writer died, the portrait—which now hangs in the Metropolitan Museum of Art—would remain as the permanent representation of her.

Eleanor Roosevelt by Daniel E. Greene Daniel E. Greene

Most portraits don't find their way into museum collections, but thousands of them are commissioned each year as a way of honoring a family member or official. They hang in homes, universities and offices (and may eventually sit unseen in closets, attics and unused guest rooms of distant relatives).

For those looking to have a portrait done, the most central resource is Portraits Inc. (www.portraitsinc.com), which represents 150 artists and arranges approximately 500 portrait commissions annually. According to Julia G. Baughman, executive partner, prices range from $10,000 to $100,000, based on the size of the portrait (head-and-shoulders, three-quarter length or full-length) and the medium (charcoal, pastel or oil paint). The average commission is $20,000 to $30,000. The price is much cheaper—$3,000 to $10,000—for those who want a portrait of their pet.

Eager to Please

Many people prefer to find a portraitist through word-of-mouth referrals or after seeing a portrait hanging in someone's home or office.

A bronze bust of former President George H.W. Bush by Marc Mellon. Marc Mellon

Not long after President George W. Bush left office, he and his wife were having dinner at the Dallas home of their old friends Annette and Harold Simmons<phrase name="Simmons, Harold" seoname="" significance="PROMINENT" type="PERSON" topicid="" vrtysux="PERSON|Simmons, Harold"> , according to David Sherzer, the former president's office manager. The conversation turned to the nearby Southern Methodist University, which was building a school of education named for Annette (based on the Simmons' $20 million gift to the university in 2007) and where Mr. Bush was setting up a presidential library. Ms. Simmons mentioned that John Howard Sanden would be painting the portrait of her that would hang inside the school. The Bushes were looking for someone to paint the former president's official White House portrait and asked Ms. Simmons whether Mr. Sanden was easy to work with. She offered profuse praise, Mr. Sherzer and other sources say, and within a few weeks a staffer in the Bush presidential library contacted Mr. Sanden. The portrait that ensued now hangs in the White House.

One of the first questions people ask when seeking a portraitist is, "Is the artist easy to work with?"

Portrait of former New York Gov. Mario Cuomo by Simmie Knox. Simmie Knox

That often means this: Will the artist take suggestions or make changes? Those being painted often are highly conscious of how they appear to others, and they may be used to giving orders, not giving in to artistic egos.

Raymond Kinstler ($30,000-$100,000 per portrait) says one of his most difficult subjects was actress Katharine Hepburn because "she was very opinionated. She had very strong ideas about her persona and questioned me about every brush stroke. I would carefully explain what I'm doing, but at one point she told me, 'You talk too much. Why don't you paint a little more?'"

Renowned painter and portraitist John Singer Sargent, whose "Portrait of Madame X" is in the permanent collection of the Metropolitan Museum of Art, once defined a portrait as "a picture of someone who has something wrong with his mouth," meaning that people are often dissatisfied with their mouth, ears, nose or other feature and take it out on the artist painting them.

'Make Me Thin'

"A lot of subjects tell me, 'make me thin,' and they try to make a joke of it, but they really mean it," says Nelson Shanks ($85,000-$350,000 per portrait), an artist who has painted Supreme Court justices, presidents and one pope, among others.

Since the portrait commission of an important individual usually arrives at the end of that individual's career, it isn't uncommon for artists to portray their subjects a few years younger. "You want to paint not the wizened old guy in front of you but the guy who built the company," says Jacob Collins ($100,000 per portrait).

Portrait of a young woman by Daniel E. Greene. Daniel E. Greene

Robert Anderson of Darien, Conn., who painted former Yale chaplain William Sloane Coffin, among others, says that while he has been known to trim 20 pounds or so off some of his subjects, he tries not to stray too far from what is in front of him. If the portrait isn't true to life, he says, "you might insult someone who says, 'That was my favorite wart you left out.'"

Sometimes a portrait portrays the subject's achievements, such as a doctor shown in surgical scrubs or a young woman in equestrian gear, or brings out an aspect of the individual's personality that hasn't been captured before.

Simmie Knox's portrait of Supreme Court Justice Thurgood Marshall, for instance, shows him smiling. One would be hard-pressed to find many published photographs of that. ("The only thing I don't like about this portrait," Justice Marshall said jokingly to Mr. Knox, is, "I always wanted to be portrayed as a hanging judge.")

Of course, most commissioned portraits aren't of famous and powerful people. They are of family members and are destined to hang in private homes.

"The majority are of children, little girls in white dresses," says Daniel E. Greene, a portrait artist in North Salem, N.Y. Sittings are more of a challenge with children, he says, because "it is hard to get them to sit still." In those cases, Mr. Greene might work from a photograph taken on location, though even then, "you have to chase the child around" to get the picture, he says.

And don't think famous people are the only ones who go to great lengths to make sure they are portrayed looking their best.

Mr. Greene remembers a woman in St. Kitts who made a big production out of his visit to her house. He says she had on hand "a seamstress, a makeup person, a hairdresser and someone to iron her clothes" in order that everything look perfect. "The portrait turned out very nicely," he says.

Mr. Grant is a writer in Amherst, Mass. He can be reached at reports@wsj.com.