Often, obituaries of our immigrant ancestors will be found in ethnic newspapers.
One way to locate microfilm of old newspapers is by using WorldCat.. through the Library's website.
Search for the name of a town as a subject, and the keywords newspapers and the name of an ethnic group. Remember to click on limit type to "serial publications."
Here is the result of a sample search for Chicago (Ill.) Polish newspapers.
Click on Libraries Worldwide to see which libraries have the newspaper you need.