A Ellis Island is the best-known US immigration port, so many people assume their ancestors arrived there.
Don’t stop your search at Ellis Island. Boston, Baltimore, New Orleans and San Francisco also were major immigration ports, but immigrants could arrive in just about any coastal city.
You didn’t say what year your grandfather came to America. Ellis Island opened in 1892 and closed in 1954. And the passenger database you searched covers only arrivals from 1892 to 1924 (you can find this information in the site’s search tips).
Sometimes database creators had a hard time reading the original records, so passengers’ names might be misspelled. If you’re sure your grandfather arrived at Ellis Island, search for alternate spellings, or use Stephen P. Morse’s Ellis Island One-Step search form.
What if you don’t know the port? You can narrow the possibilities by researching his life in the United States. You also may get lucky with a searchable immigration database. The subscription site Ancestry.com has one; a version called Ancestry Library Edition is free at many libraries.
My quick Ancestry.com search returned a Canadian border-crossing record (below) for an Anthony Borges born in 1904 in St. Marie in the Azores. This man arrived first in Canada and traveled to Niagara Fall, NY, on Sept. 7, 1933.
This was the first of many matches for people named Antonio Borges, so if the man in this record isn’t your grandfather, try an Ancestry.com search.