These two sisters came across around 1880-1882 from, possibly, Kristiana. I am looking for anything that might help me establish their home(s) in Norway.
A bit more information about the women in the U.S. might be helpful to find the where in Norway...
What did their profiles look like in the US 1900 census? That census asks the month and year of birth and the year date of migration--those dates might be useful.
Did these women marry and did they have children? Did other relatives of theirs come to America? Its much easier to find a family than it is to find a single person.
If you look at the database of emigrants leaving Kristiania 1871-1930 (and the one for Oslo 1867-1930) you can find about 20-27 women leaving from that port with names like Josephine Jacobsen (and including spelling variants for those names). But there is no way to know which might be YOUR girl or woman without additional identification. Perhaps you'd prefer to search those databases yourself. http://www.rootsweb.ancestry.com/~norway/DigitalArchives.html