Non-Armigerous
Non-Armigerous simply means awards or ranks that do not confer the right to bear personal arms. That is to say, the award does not carry with it an Award of Arms, Grant of Arms, or Patent of Arms.
There are many awards that are non-armigerous, such as the King's Favor pr Forget-me-not. A few are considered very high awards, and even confer precedence, such as the Lion of An Tir.