UPDATE, 2:45 pm: University of Richmond School of Law professor Kevin Walsh is claiming that Justice Scalia's headgear is actually a replica of a hat worn by St. Thomas More. It was a gift to Scalia in 2010 from the St. Thomas More Society of Richmond, Virginia for his participation in the society's Red Mass and dinner.
Supreme Court justices at today's inaugural ceremony appear to be wearing a variety of headgear, but Justices Antonin Scalia and Stephen Breyer seem to be the ones carrying on the tradition of wearing black cornered skullcaps.
The skullcaps have gone in and out of vogue with the justices since the early 20th century. They are not for inaugurals only, and have been worn by justices at public events in cold weather for decades. Four justices wore them at the laying of the Supreme Court cornerstone in 1932.
The skullcaps have been occasionally associated with British judicial garb since the 15th century, but no one seems certain whether there is a direct line between that usage and the current-day justices. Chief Justice Edward Douglas White wore one when swearing in President Woodrow Wilson in 1913, the first time a skullcap was documented in an inaugural photo. Chief Justice William Howard Taft also wore a skullcap during the ceremonies for Presidents Calvin Coolidge and Herbert Hoover.
Their moment to shine came in 1961 for John F. Kennedy's inaugural when seven of the nine justices wore skullcaps. Memos about skullcaps can be found in the files of Justice Harry Blackmun throughout the 1970s and 1980s, with one even suggesting how they should be doffed and held during the National Anthem. But the caps were not worn widely again until William Rehnquist, a history buff, became chief justice in 1986. In 2005, Breyer and Scalia wore them. In 2009, under the new chief justice John Roberts Jr., only Scalia did so.