The heirs of a Jewish Dutch family, which lost one of the finest art collections in pre-World War II Amsterdam to the Nazis, received some restitution yesterday when a sculpture that once belonged to them sold for about $4.5 million.

“Borromeo Madonna,” a 15th-century relief by the Early Renaissance artist Donatello, was bought by the Kimbell Art Museum in Fort Worth, Texas, at Sotheby’s Old Masters painting auction in New York.

For the heirs of Jacques Goudstikker, a prominent Jewish dealer and collector who was killed fleeing Amsterdam in 1940, yesterday’s sale is only part of what could be a long-awaited week of restitution. Goudstikker’s American-born granddaughter, Marei von Saher, of Greenwich, Conn., has been fighting for almost a decade to gain recognition for his collection in prominent Dutch museums, where more than 250 of the artworks he once owned now hang, as well as compensation from the government for some of his lost works.

The Donatello sold yesterday was not part of the Goudstikker collection controlled by the Dutch government. According to Sotheby’s catalog, the anonymous owner of “Borromeo Madonna” and the Goudstikker heirs came to an agreement before the auction on the sale’s proceeds. Ms. von Saher’s lawyer, Lawrence Kaye, of Herrick, Feinstein, would not comment on how much of the proceeds will go to Ms. von Saher.

Mr. Goudstikker’s pre-World War II collection comprised an estimated 1,400 works, including several by old masters like Rembrandt, Rubens, Goya, and Raphael. According to previous reports, Nazi leader Hermann Göring bought nearly 800 of the paintings, and his agent Alois Miedl purchased the remainder soon after the Nazis began to occupy Amsterdam. The whereabouts of most of the collection is still unknown.

Mr. Kaye, told The New York Sun yesterday the family was awaiting a decision by the Dutch government on restitution for the works now in the hands of Dutch cultural institutions. The collection is estimated to be worth millions of dollars.

Recently, a Dutch restitution committee, which examines claims for property seized in the Holocaust, reached a decision on Ms. von Saher’s claims and made a recommendation to the Dutch ministry of culture, which is expected to announce a decision next week.

“It is a very, very valuable collection,” Mr. Kaye said. “My understanding, based on what the ministry is saying, is that there will be a decision by next Friday.”

The ministry of culture has previously resisted Ms. von Saher’s claims, arguing that after Goudstikker’s death, his collection was voluntarily sold to Göring for more than $10 million. Representatives of Ms. von Saher have said that the sale was made under duress, perhaps out of fear of death or banishment to a concentration camp.

After the war, according to news accounts, Goudstikker’s widow, Desiree, could have bought back some of the collection that had been recovered, but did not do so because of the great expense. She renounced her claims to the works, but she expressed frustration over the arduous process that would have been required to recover the collection.

The work sold yesterday has an equally long history. According to Sotheby’s, the relief adorned a church in a small village in Italy until 1902, when it was sold to buy an organ. “Borromeo Madonna” turned up in a famous Amsterdam collection in 1925, before it came into Goudstikker’s possession by 1928. It disappeared until it resurfaced in Germany in 1989, covered in layers of paint and stucco, and unrecognizable as the work of an old master. The current anonymous owners had the relief restored and identified as Donatello’s work.

In a statement yesterday, Ms. von Saher said: “We are delighted to have participated in the sale of this extraordinary sculpture and are gratified that the sale confirms that Jacques was correct when he attributed this work to Donatello 80 years ago. It is a credit to his eye as a connoisseur that he saw this at a time when the resources to verify such attributions did not exist.”