String handling isn't very consistent between different versions of SQL. The exact syntax will depend on what SQL engine you are using, but it is definitely possible.
If you can settle for a "loose match" that might be confused by special characters like _ and %, you could use concatenate percent signs at the begining and end of your "search for" column, and use that as the LIKE pattern. This is reasonably portable, but it still depends on the string concatenation syntax (which varies from one SQL engine to another).
-PatP