He married Elizabeth Huntington on 16 November 1750 in Windham, Connecticut, and she died on 17 December 1773; Davenport remarried to Martha Fitch on 8 August 1776 in Stamford.

In the aftermath of the American Revolutionary War, Davenport took ill and wounded US soldiers into home to care for their recovery.

[3] In his 1866 poem "Abraham Davenport" (Tent on the Beach),[2] the Quaker poet John Greenleaf Whittier lauded the legislator: "And there he stands in memory to this day, Erect, self-poised, a rugged face, half seen Against the background of unnatural dark, A witness to the ages as they pass, That simple duty hath no place for fear.

"[3] In November 1934, Delos Palmer—working under a Works Progress Administration commission—painted a Dark-Day mural of Davenport and Connecticut Governor Jonathan Trumbull in the Stamford city courtroom.

At its dedication, Judge Charles Davenport Lockwood said the art "should be an inspiration and a lesson during these days of hard times [the Great Depression]."