can UNIQUEness of TEXT datatype really be guaranteed?

I am in the process re-implementing some pgsql table declarations into a MySQL database. I have this one line where I say
...
fieldname TEXT UNIQUE,
...
in my pgsql table because I want to ensure that no one enters the same thing in this field and I didn't choose VARCHAR type because I have no idea how possibly long I might need to let the field be...

... but MySQL doesn't like this because a TEXT datatype is considered a BLOB that can't be indexed and it can't guarantee will be UNIQUE apparently...

So I can't help but wonder, can Postgres really guarantee a TEXT field to be UNIQUE... or is declaring a TEXT field UNIQUE something an uninformed, novice user would do?... or is it something indicative of the strength and/or weeknesses that separate the functionality of the two DBMSs.

Ferindo Middleton