What site do you use that supports exact searching?
Google supports this. I also use this capability daily.
You can search with quoted strings but the results you get don't need to have that string.
On Google you do.
There is some stemming performed but otherwise quotes are honoured. If you come across a query that matches no results, there should be a message in the results saying so, and that it fell back to non-quotes.
fwiw I work in Mojeek.
However, I won't be switching because it doesn't support exact searching (e.g. via double quotes). Add that and I might consider it - I need that feature often.