I think the only way you will find this if you utilize local genealogy databases for communities or churches.Even if using a paid subscription to something like Ancestry, you can get so many hits that research is difficult.It depends on the popularity of the name.
You can reduce the number of results by using additional search terms such as:
[ Zawertany +genealogy ] [ Zawertany +Catholic +Warsaw ] [ Zawertany +Orthodox +St. Petersburg ] [ Zawertany +Schulc +Russia ] (in this case Schulc might be the surname of a spouse or mother) [ "Paul Zawertany" +Russia ]
You can also eliminate terms.If someone with that surname does a lot of advertising for his company, you could go:
[ Zawertany +genealogy -realty ]
Hope this helps.Of course replace names and terms to suit your situation.Note that the length of your search terms will reduce your results but eventually you could start missing valuable ones because of the particular content.Also, Google relies to a large extent on accurate spellings (though sometimes it offers options).Be sure to consider variant spellings of surnames and places in your search.