Openshaw had a son and daughter with his wife, Selina Gertrude Pratt, the daughter of William Pratt of Buern Abbey in Oxford, whom he met at the London Hospital where she had trained as a nurse. They married in 1890.
His son, Major L.P. Openshaw, served in the Royal Air Force as a pilot and was killed in a mid-air collision during an air show in Bournemouth in June 1927.
A few months after his wife's death in 1929 Openshaw developed diabetes and died of pneumonia in a nursing home aged 73.
Openshaw’s photographs from the Second Boer War, his medals and certificates were donated to the Royal London Hospital Archives and Museum in 2004 by John Jenner, his grandson.