Robertson was born in Liverpool in 1838 as the fourth daughter of Justice Charles Crompton.
[3] They were both involved in social work and they were members of the National Society for Women's Suffrage.
Her mother had been active in working for improving the provision of education for women and this was a cause which she shared.
[3] She understood money and finance so she applied for the position of secretary of Girton College when it was created in 1877.
One thousand pounds was left to the New Hospital for Women to create the "Caroline Croom Robertson" bed.