She won the female Dutch Chess Championship ten times (1937, 1939, 1946, 1948, 1950, 1952, 1954, 1956, 1958 and 1961). Heemskerk won a match against Catharina Roodzant 4.5 : 0.5 in 1937, and lost a match to Sonja Graf 0 : 4 in 1939 in Amsterdam.
She played in the 1st Women's Chess Olympiad at Emmen 1957 – but had to withdraw after only two days upon learning her father had died.[6] In 1989, at the age of 70 she participated in the Moscow GMA qualifiers alongside strong male Grandmasters.[7]