In a Google search for "Eggleston McGee Outagamie," I came across a web page for the "Gleanings" of the Fox Valley Genealogical Society. In the "E" and "M" listings, there are entries for Sarah Maria Eggleston and James Edwin McGee, who were married on 2 July 1865, according to an article or notice published in the Appleton Crescent (one of the forerunners of today's Appleton Post-Crescent) on 8 July 1865.
Knowing when and where the marriage took place should make it easier to obtain a copy of the original marriage record via the Outagamie County Register of Deeds office. The Appleton Public Library can also provide you with a copy of the 1865 newspaper item.
Good luck in your search!