WASHINGTON — Police officers in Los Angeles stormed Augusta Millender’s home early one morning in 2003. They were looking for Ms. Millender’s foster son, Jerry Bowen, and for a shotgun he had used in a domestic assault.

They found neither. But they did seize a gun owned by Ms. Millender, who was 73. The gun was legal, and she said she kept it for self-defense.

The Supreme Court heard arguments on Monday in Ms. Mellender’s lawsuit against the police for what she said was a violation of her rights under the Fourth Amendment, which protects against unreasonable searches and seizures. Both the National Rifle Association and the American Civil Liberties Union filed briefs supporting her position.

The police had obtained a warrant to search Ms. Millender’s home, but lower courts ruled that it violated the Fourth Amendment because parts of it were not supported by probable cause. In particular, they said, the warrant improperly allowed the police to search for “all handguns, shotguns and rifles” and “evidence showing street gang membership.”