“If I get locked up, will you bail me out?” Ms. Ferreira asked her friends.

Ambergris begins as a waxlike substance secreted in the intestines of some sperm whales, perhaps to protect the whale from the hard, indigestible “beaks” of giant squid it feeds upon. The whales expel the blobs, dark and foul-smelling, to float the ocean. After much seasoning by waves, wind, salt and sun, they may wash up as solid, fragrant chunks.

Because ambergris varies widely in color, shape and texture, identification falls to those who have handled it before, a group that in a post-whaling age is very small. Ms. Ferreira says she has yet to find an ambergris expert.

“A hundred years ago, you would have no problem finding someone who could identify this,” said James G. Mead, curator of marine mammals at the Smithsonian Institution, who said he hears of new ambergris surfacing somewhere in the world maybe once every five or six years. “More often, you have people who think they’ve found it and they can retire, only to find out it’s a big hunk of floor wax.”

Adrienne Beuse, an ambergris dealer in New Zealand, said in a telephone interview that good-quality ambergris can be sold for up to $10 per gram, adding that for the finest grades, “the sky’s the limit.”

At $10 per gram, Ms. Ferreira’s chunk, according to a neighbor’s kitchen scale, would have a value of $18,000. “The only way to positively identify ambergris is to have experience handling and smelling it, and very few people in the world have that,” Ms. Beuse said. “Certainly, if she has it, it’s like winning a mini-lottery.”

Larry Penny, 71, director of East Hampton’s natural resources department, said he had no way of making a definite determination, because “we don’t keep a certified whale-vomit expert on staff.”

Mr. Penny, whose great-great-uncle was skipper of a whaling ship out of Sag Harbor, said he grew up searching the beach for ambergris.