MONTAUK, N.Y. — In this season of strange presents from relatives, Dorothy Ferreira got a doozy the other day from her 82-year-old sister in Waterloo, Iowa. It was ugly. It weighed four pounds. There was no receipt in the box.

Inside she found what looked like a gnarled, funky candle but could actually be a huge hunk of petrified whale vomit worth as much as $18,000.

“I called my sister and asked her, ‘What the heck did you send me?’ ” recalled Ms. Ferreira, 67, who has lived here on the eastern tip of Long Island since 1982. “She said: ‘I don’t know, but I found it on the beach in Montauk 50 years ago and just kept it around. You’re the one who lives by the ocean; ask someone out there what it is.’ ”

So Ms. Ferreira called the Town of East Hampton’s department of natural resources, which dispatched an old salt from Montauk named Walter Galcik.

Mr. Galcik, 80, concluded that the mysterious gift might be ambergris, the storied substance created in the intestines of a sperm whale and spewed into the ocean. Also called “whale’s pearl” or “floating gold,” ambergris is a rare and often valuable ingredient in fine perfumes.

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