Hi - looked for Søren Pedersen/Petersen in the emigration lists from Denmark. Used the site Danish Demographic Database (www.ddd.dda.dk). Did not find him in 1863, 1864, 1865. Many immigrants do not appear on that list.
I also looked for him on Danish Demographic Database searching the census records. It's slow going and I think maybe you might want to learn how to do it so you can continue what I did?
Also at Danish Demographic Database I searched 1840 census for S%ren Pe%ers. The % is a wildcard, so this allows for various ways of including the ø in Søren, for the spellings PeTersen and PeDersen, and for both the -sen and -son endings (although in Denmark it would almost always be -sen). I neglected to allow for a middle name (if he appeared as Søren Vilhelm Pedersen I'd have missed him). One chooses a range of ages in 1840, and I chose age 1-9. In 1840 I would be able to find both boys (Søren and brother Anders). There are a bazillion Søren Pedersens of about the right age but not very many with a brother Anders of about the right age difference. (The larger the number of connections, the fewer the people who are going to meet the criteria).
A couple of possibilities turned up and I posted below, and I can't continue the search right now but hope perhaps you will.
1840 Ribe, Skast, Faaborg, Aggerbek Bye [Agerbæk], , En Gaard, 5, FT-1840 Peder Jensen 38 Gift Gaardmand Sindel Marie Sørensdatter 32 Gift Hans Kone Jens Pedersen 9 Ugift Deres Børn Søren Pedersen 7 Ugift Deres Børn Johanne Kjerstine Pedersen 5 Ugift Deres Børn Mette Pedersen 3 Ugift Deres Børn Anders Pedersen 1 Ugift Deres Børn Johanne Mogensdatter 28 Ugift Deres Tjenestepige (servant girl)
1840 Randers, Galten, Vissing, Vissing Bye, , en Gaard, 30, FT-1840 Peder Andersen Smed 33 Gift Gaardmand Ane Marie Sørensdatter 37 Gift Kone Rasmus Sørensen 8 Ugift Barn Søren Christjan Sørensen 7 Ugift Barn Søren Pedersen 6 Ugift Barn Anders Pedersen 2 Ugift Barn Ane Kirstine Pedersdatter 1 Ugift Barn Niels Nielsen 25 Ugift Tjenestekarl (servant man) Caroline Rasmusdatter 19 Ugift Tjenestepige (servant girl)
Once you have narrowed down the candidates in some way - the forum will be better able to help you. There is also help at a site called Slaegt og Data DIS-Danmark "Find Your Relatives in Denmark."
Another way to narrow the candidates is to identify more siblings; a more specific bith date for anybody/everybody; to share the names of the children (Danes named their first born after the father's father and father's mother, then after the mother's father and mother, although this was not law and was varied). Would be good if you can dredge up more information in county genealogical societies, the Danish Lutheran Churches in the area, etc. but I am assuming you've tried all that. People who want to help you will ask questions such as "Do you have his death certificate? marriage certificate? Are his parents' names listed there?" Be prepared for these questions by including the answers in your original post if you post again.
If you do search on your own in the Danish records, do not be surprised by turning up a family in which the father is not named Petersen. Likely the name of Anders's and Soren's father is Peter/Peder with some other patronymic last name. Probably you know this.
Another way to search is via FAMILY SEARCH, and you are probably familiar with that, so I did not try it.
Ancestry.com is the best US database and may be available at your local library. (Probably is available to you there)
Okay, I did not turn up Soren immigrating but here is a candidate for Anders immigrating, below. There are quite a few more Anders Petersens on the ddd.dda.dk emigration list of the right age immigrating at the right time. I chose this one arbitrarily because he says he's going to Berlin, Wisconsin. But immigrants who state they are going to "New York" or "America" could also be headed ultimately for Wisconsin.
Navn: Petersen, Anders Stilling: Landmand Alder: 29 Bestemmelsessted: Berlin, Wisconsin Kontrakt nr.: 199100 Forevisningsdato: 4/14/1869 Sidste oph.sogn: Sonnerup Sidste oph. amt: København Sidste oph.sted: Sonnerup pr. Roskilde Bestemmelses land: USA Bestemmelses by: Berlin Bestemmelses stat: Wisconsin Skibsnavn: Indirekte IDkode: I6969P1516
Again, he's only one candidate. The trick is to find pieces that "fit" together. I didn't find this Anders in the census - I tried, so I could see if he had a brother Soren of the right age.