The U.S. Supreme Court has generally upheld the First Amendment protection of a free press to a great extent. This means that it has allowed very little (almost no) censorship of the print media. The Court has consistently recognized the vital role of the press in a democratic society and has placed a high value on protecting freedom of expression, including the freedom of the press.
Examples of Supreme Court cases that have reinforced this protection include New York Times Co. v. United States (1971), also known as the "Pentagon Papers" case, where the Court ruled in favor of the press's right to publish classified government documents, emphasizing the importance of a free press in serving as a check on government power.
Overall, the U.S. Supreme Court has taken a strong stance in upholding the First Amendment rights of the press, limiting government censorship and emphasizing the importance of a free and independent media in a democratic society.