Jewelry, of course, has an intrinsic value. It’s made of gems like diamonds, emeralds, rubies and sapphires and set in metals like platinum, gold and silver that are valuable in their own right. Many pieces also have sentimental value, having come from family members or been given on a special occasion.

But the pieces with the most investment potential have a level of craftsmanship in addition to scarcity that makes them stand out from the beautiful baubles that are produced year after year — and appreciate beyond the value of their metals and gems. These are not the run-of-the-mill pieces that mall jeweler might sell. In fact, people buying these pieces would be hard-pressed to see significant appreciation over time.

“You can melt the metal and take out the stones, but when you talk about collectible jewelry, you want to make sure the provenance of the piece is provable,” said Muffie Potter Aston, a New York socialite and former executive vice president of marketing and advertising for Van Cleef & Arpels.

She singled out a pink tourmaline ring designed by Paloma Picasso for Tiffany. When she showed it to an appraiser, she said, “He said you couldn’t buy that pink tourmaline alone today for what you paid for the ring 10 years ago.”

Alison Minton, a philanthropist in Manhattan, bought a limited edition Alhambra necklace by Van Cleef & Arpels in malachite 10 years ago. The clover style of the necklace has become well known, but the company made only 100 of the necklaces and numbered each one. Ms. Minton sold it recently for more than $12,000, which was double what she had paid for it.

“It was a great investment, and I wore it,” she said.

From her grandmother, who was part of the family that founded Bloomingdale’s, she inherited a rarer piece of jewelry — with a better story. In 1964, her grandmother went to the World’s Fair in Queens; when she came home, her apartment had been burglarized and her jewelry was gone. Instead of trying to replace the stolen items, she bought a single piece: an 18-karat gold bracelet with rubies and sapphires from Tiffany.

It cost about $400 at the time. When Ms. Minton took it to Tiffany for a repair in 2002, the jeweler valued it at $9,000. “I don’t know what it’s worth today,” she said. “I don’t wear it often because it’s so special.”

In the annals of rare jewelry for sale sits Pope Paul VI’s ring and cross. After the pontiff addressed the United Nations General Assembly in 1965, he donated his diamond-encrusted papal ring and diamond and emerald cross to the U.N., so they could be sold to help the poor. At one point, the stunt driver Evel Knievel owned them.

Bill Rau of M.S. Rau Antiques said he had acquired the set through a couple in North Carolina. It is priced at $1.9 million.

But although the set is one of a kind — and contains what Mr. Rau estimated to be $1.1 million of stones — he has been trying to sell it since 2014, showing that even unique jewelry can also be illiquid.

Like any object, from art to cars to jewelry, the fallback position if the investment fails is to consider the aesthetics of the piece.

And that’s a benefit, because sometimes the jewelry turns out to be worth less than the value of its stones and metal because of that very same uniqueness. It could be difficult to wear or it could be valuable but out of fashion. David Webb, a jewelry maker active in the 1950s to early 1970s, designed a necklace with 682 karats of opals and used smaller emeralds and diamonds to separate the pearl-shaped stones. The 36-inch necklace is for sale at $335,000.

For people approaching jewelry for investment purposes, strategy and advice count for a lot.

First, they have to think of the brand. There are a half-dozen jewelry designers that are known worldwide for their quality. That recognition makes reselling their jewelry easier.

“Every time something from the 1920s, 1950s and 1970s from Van Cleef, Cartier, Boucheron comes up for auction, they always do significantly better than they did the first time around,” Mr. Kadakia of Christie’s said.

Of course, not all brands make great pieces all of the time (and many lesser-known designers have produced fantastic pieces, like Mr. Webb’s opal necklace, that stand out). But for the big houses, time periods matter for investing.

“Of all the periods people want to collect, I always tell them Art Deco of the 1920s and 1930s,” said Diane Lloyde Roth, owner of L’Armoire, a store in New Canaan, Conn., that has been selling investment-quality jewelry for three decades. It “was probably the most beautiful period of all in jewelry production.”

She recalled some of the pieces she sold to Anne Lichtblau, a philanthropist who died last year. Mrs. Lichtblau bought a Van Cleef mystery set ruby bracelet for $140,000 in 2003; her estate sold it at auction last year for $348,500. Mrs. Lichtblau also bought a 1920s emerald, ruby and diamond bracelet by Oscar Heyman & Brothers in 1998 for $90,000. It sold for $223,500 at auction last year.

“She always wanted Art Deco,” Ms. Roth said. “She bought what she loved, but she spent real money on jewelry.”

Scarcity is important. Colored diamonds fit into this category because they are not as plentiful as white diamonds. Ms. Minton said she bought a bracelet from Verdura that the jeweler had made as a prototype – and jokes that she keeps checking with the jeweler to make sure it hasn’t made another one.

The location where a jeweler made a piece can also affect its value. For instance, vintage Cartier pieces made in France are worth more than Cartier pieces made in New York, Ms. Roth said.

When it comes to Tiffany, which of the jeweler’s designers made the piece matters considerably. Pieces made by Jean Schlumberger in the 1950s and 60s are more valuable than other Tiffany pieces from the same time because of his style but also his limited production. And jewelry made by Louis Comfort Tiffany, son of the company founder Charles Tiffany, from the 1880s to 1910 commands a greater premium still. He is known for his stained-glass lamps and precious objects, but Mr. Rau said he made about 100 pieces of jewelry as well.

Yet that scarcity and a lack of knowledge among buyers increases the need to be aware of fakes.

“I go to the cities where people have worn Tiffany or Van Cleef through the years, and family members have sold them,” said Allison Weiss Brady, a fund-raiser in New York. “One of the keys is buying it from someone you trust,” she said. But even then, she asks for documents proving the piece’s history and also the basics on the gemstones.

Contemporary jewelry is a tougher market for buyers to predict investment potential. The top houses are still producing exceptional pieces, but given the high cost of metals and stones, many of the pieces are lighter and less intricate than a generation ago.

“When all of your raw materials go up, something’s got to give somewhere,” Ms. Roth said.

There are exceptions, like the Parisian designer JAR, the initials of Joel Arthur Rosenthal. When Ellen Barkin, the actress, sold jewelry given to her by her ex-husband, the billionaire Ronald O. Perelman, she had 17 pieces by JAR, who produces fewer than 100 pieces a year. One pair of JAR earrings at last year’s auction fetched $1.8 million.