Dodo Cheney, a daughter of tennis royalty who wore lace and pearls as she rolled through generations of competitors on the way to winning 391 tennis championships in the United States, most of them after she turned 55, died on Sunday in Escondido, Calif. She was 98.

The International Tennis Hall of Fame announced her death on Tuesday.

At her induction ceremony at the Hall, in Newport, R.I., in 2004, Cheney, who played competitively well into her 80s, chose John McEnroe to be her presenter, then hit balls back and forth with him afterward.

Cheney — who was born Dorothy Bundy and acquired the nickname Dodo in childhood — was the first American to win the Australian championships, now known as the Australian Open, a feat accomplished in 1938. She was runner-up three times in women’s doubles at Grand Slam tournaments and four times in mixed doubles.

In singles, she reached four semifinals of the United States championships and one semifinal each at Wimbledon and the French championships. She was ranked third in the United States in 1937, 1938 and 1941. Her highest world ranking was No. 6 in 1946.