Sarah Hammond Palfrey Danzig (née Palfrey; September 18, 1912 – February 27, 1996) was an American tennis player whose adult amateur career spanned 19 years, from June 1926 until September 1945. She won two singles, nine women's doubles, and four mixed doubles titles at the U.S. National Championships.

Palfrey and her siblings, including John Palfrey, Polly Palfrey Woodrow and Mianne Palfrey, competed in tennis at the national level.

She was 32 years old, married to Elwood Cooke, and a mother in 1945 when she won her second singles title at the U.S. National Championships. Pauline Betz was her opponent in the final. Since she lost to Cooke in the 1941 final, Betz had won three consecutive titles and 19 consecutive matches at these championships. In 1945, Cooke lost the first set and squandered her 5–2 lead in the second set before recovering to win it 8–6. In the third set, Betz got close to winning yet another title when she served for a 5–3 lead. Cooke, however, broke her serve and then won the next two games to win the tournament. She became only the second mother to win this title, with Hazel Hotchkiss Wightman being the first.

Cooke is one of the few women, if not the sole woman, to appear on a top-level male championship honor roll. Because of the manpower crisis during World War II, she and husband Elwood were permitted to enter the men's doubles at the 1945 Tri-State Championships in Cincinnati. They lost in the final to Hal Surface and Bill Talbert.

Palfrey won 16 Grand Slam championships in women's doubles (11) and mixed doubles (5). She teamed with Betty Nuthall to win the 1930 U. S. National Championships and with Helen Jacobs to win the 1932, 1934, and 1935 championships. Palfrey and Alice Marble won the U. S. National Championships from 1937 through 1940. At the Wimbledon Championships, Palfrey and Marble won the 1938 and 1939 women's doubles titles. Palfrey's last U.S. women's doubles championship was in 1941 with Margaret Osborne. In mixed doubles, Palfrey teamed with four different partners to win the U.S. National Championships: Fred Perry (1932), Enrique Maier (1935), Don Budge (1937), and Jack Kramer (1941). Palfrey also won the mixed doubles title at the 1939 French International Championships, teaming with future husband Elwood Cooke.

Palfrey and Marble were undefeated in doubles from 1937 until Marble turned professional at the end of 1940.

In 1947, Cooke and Betz went on a "barnstorming" tour of mostly one-night stands in the U.S. and Europe, with each earning about US$10,000. They had been stripped of their amateur status by the United States Lawn Tennis Association (USLTA) in early 1947 because Elwood Cooke had written letters to several tournament organizers about creating a professional tour.

According to A. Wallis Myers of The Daily Telegraph and John Olliff of the Daily Mail, Palfrey was one of the 10 highest ranked women in the world from 1933 through 1936 and in 1938 and 1939. Her career high was fourth in 1934. (No world rankings were issued from 1940 through 1945.)