Hi. Just to recap - You need a marriage record and parents for John Frederick Petersen (born in Denmark on June 24, 1864) and Marie Christana Olsen (born in Denmark in 1864). Did a search for you on Ancestry.com, Dansk Demografik Database, and Family Search. Collected some census information along the way. Sounds like you have it, but doesn't hurt to post it.
At the bottom is a possible immigration for Marie. Very iffy.
FAMILY SEARCH transcription of MARRIAGE RECORD 21 Sep 1889 Wausaukee, Marinette, Wisconsin Groom: John August Fred Peterson Bride: Mary Olson Groom's father: John Fredrick Peterson Groom's mother: Amelia Peterson Bride's father's name: Oley Andersen Bride's mother's name: Betsey Andersen M00351-7 Wisconsin-EASy film 1292021
1900 Wausaukee, Marinette, Wisconsin John Peterson35 born Jan 1865 in Denmark; immigrated in 1887 married 10 years; railroad section laborer Mary Peterson36 born Nov 1863 in Denmark; immigrated 1889; has had 5 children and 5 are living Matilda Peterson9 Amelia Peterson7 Day* Peterson5 Mary Peterson4 Gertrude Peterson1
1905 (01 June - Wisconsin State Census) Athelstane, Marinette, Wisconsin John Peterson40 Marie Peterson40 Mathilda Peterson14 Amalie Peterson12 Dagny Peterson10 Mary Peterson8 Gerthre Peterson6 August Peterson4 Emma Peterson1
1910 Athelstane, Marinette, Wisconsin Mrs Mary C Petersen45 b 1865 in Denmark; has had 8 children and 8 are living; immigrated 1889; farmer/general farming Dagmar O Petersen15 Mary Petersen13 Gertrude F Petersen11 August F Petersen9 Emma L Petersen6 Louis S Petersen4
1920 Athelstane, Marinette, Wisconsin Mary Petersen55 b 1865 in Denmark; immigrated 1890 F Gertrude Petersen21 F August Petersen19 B Mary Petersen23 S Louis Petersen14 T Emma Petersen16 S Glendon Petersen3[3 4/12] NEPHEW
Marie Christine Olsen is a common name in Denmark. If she traveled alone (sounds like she did or you are not sure), then it is hard to identify her by way of her companions. Below is one possibility - but the match is not exact - and there is no special way to identify her.
EMIGRATION: Departure from Denmark Navn:Olsen, Marie Stilling: Jomfru (= unmarried woman) Alder: 26 Bestemmelsessted:NY. (= destination) Kontrakt nr.: 234500 Forevisningsdato: 12/4/1889 Fødested: ?Fødesogn: ?(= birthplace) Sidste oph.sogn: Vålse (Falster)Sidste oph. amt: Maribo Sidste oph.sted: Vaalse, Maribo(= last residence) Bestemmelses land: USA Bestemmelses by: New York CityBestemmelses stat: New York State Skibsnavn: Island IDkode: D8991O0106
IMMIGRATION:Arrival in USA Name:Marie Olsen Arrival Date: 30 Dec 1889 Birth Year: abt 1863 Age: 26 Gender: Female Ethnicity/Race/Nationality: Danish Place of Origin: Denmark Port of Departure: Christiania and Christiansand, Norway and Copenhagen, Denmark Destination:United States of America Port of Arrival:New York Port Arrival State:New York Port Arrival Country:United States Ship Name:Island