Ixquick not even "does search". It is a meta search engine. See, for
instance, its "about" page:
When you search with Ixquick search engine, you are searching many popular
search engines
As to "links to non-free websites", I assume you mean presenting, as results
to a query, links to websites of non-free software (or do you want the Web to
be published under a free license?!). I do not believe such a Web search
engine exists. First of all, it looks impossible: we would need to manually
read the whole Web to detect sites proposing non-free software. Then a
website may host non-free software (or be made of non-free Javascript, is it
what you meant?) but, besides, has useful informal that you read/watch
without downloading the non-free code (or executing the non-free Javascript).
But maybe you wanted to talk about privacy... Actually I should stop writing
and let you clarify what you meant! :-)