In autumn 1780, he became surgeon on board the privateer sloop Hope owned by Joseph Nightingale and John Innis Clarke, keeping a diary that was later published.

Drowne was discharged from the 1st Rhode Island Regiment on June 15, 1783, receiving a Badge of Merit for six years' faithful service.

In 1783, Drowne was elected to the Brown University (then still known as the College in the English Colony of Rhode Island and Providence Plantations ) board of fellows.

He traveled to Europe, touring various medical facilities and schools and meeting Benjamin Franklin and Thomas Jefferson in Paris.

Returning home, he practiced medicine in Providence, Rhode Island until 1788, when he settled in Marietta, Ohio with other war veterans.

The first honorary Doctor of Medicine degree from Brown Medical School was conferred upon Solomon Drowne in 1804.