Websites that allow users to search digital images of newspapers are great. They can make the discovery of newspaper references take seconds instead of the hours, days, or months, it would take to manually search a specific set of newspapers.
But make certain that the site has the actual images of the time period you need–month, year, etc. If the newspaper was daily and you need an item that probably was printed in March of 1888, does the website have all the issues from that month? Do you know how to browse their set of images to find out?
Issues may be missing from that time period. You may not be searching all the issues you think you are.