You may want to check with Menominee County Library, they have the Menominee County Journal Obituaries list 1893 - 2009 on there web site. http://joomla.uproc.lib.mi.us/Menominee/
You can check and see if they still do obit. lookups. I don't know if there is a fee.
I have found the spelling Eckman and Ekman.
Found on the obituaries list John Ekman d. 4 Feb 1934, Daggett, MI
Also found a marriage date 27 Apr 1891 Daggett, Menominee, MI for John Ekman and Theresa Olson, her parents are listed as John Olson and Tillie Petterson, John's parents Jonas Ekman and Johanna Pearson. This is on www.familysearch.org
There are death records 1897 - 1920 on www.seekingmichigan.org
Orpha Ekman d. 28 May 1908
Warner Ekman d. 9 Oct 1918
Lillian Ekman b. 20 Oct 1898, d. 9 Sep 1909
Johanna Ekman b. 25 Mar 1831 d. 23 Jun 1920 maybe John Ekman's mother.
Check both spellings.
Hope this help get you Obits.