Even after the introduction of the civil registration, but especially in earlier records, there may be spelling variations of a name. A woman may be called Elizabeth or Elisabeth, her last name might be written as Jansen or Janssen.
Especially since most Dutch search engines only find exact matches, it is important to try different spelling variations or use wildcards. A search for Eli* Jans* would have found all four variations of the name.
If you can’t find a person, also search for records of their spouse, or try searching for just the last names of both spouses.