We complement two papers on supertropical valuation theory ([IKR1],[IKR2]) by
providing natural examples of m-valuations (= monoid valuations), after that of
supervaluations and transmissions between them. The supervaluations discussed
have values in totally ordered supertropical semirings, and the transmissions
discussed respect the orderings. Basics of a theory of such semirings and
transmissions are developed as far as needed.