For those who were unaware, FamilySearch has a database, United States Census of Union Veterans and Widows of the Civil War, 1890, that may help those whose Union veteran (or widow) who lived until 1890. The census is not entirely extant and only includes states alphabetically from Kentucky through Wyoming.
If you know your ancestor owned real property at their death and you can’t find a probate, check for a partition suit among the heirs. Those suits should list all the heirs and may clearly delineate the relative portions of the estate they received. Even if the portions they get are not listed, the relative amounts of money they get may help you determine relationships. In the United States, these would local county court records. This partition suit from 1924 is being analyzed in an upcoming issue of Casefile Clues. 
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