erfüllen / ausführen
Explanation:
die Zielvorgaben erfüllen, den Zielvorgaben der Mission (Produktivität) entsprechen, die Mission erfolgreich ausführen
also ein bisschen stäker als dahinterstehen.
oder
die Richtlinien der Mission (Produktivität) erfolgreich einhalten
wie: stand behind our commitment of quality and service:
http://www.aquaticsystems.com/mission.html
ähnlich wie das von dir vorgeschlagene "Wort halten"
"stand behind" besagt hier m.E. in erster Linie, dass man durch das Sicherheitsnetz des Service-Vertrags die (Ziele der) Mission voll und ganz erfüllen kann, dieser/diesen gerecht werden kann.
live up to it wäre ähnlich --
der Mission gerecht werden
der Mission entsprechen
wörtlicher vielleicht:
für die (Ziele der) Mission einstehen können,
here very similar to:
http://www.answers.com/stand by
stand by
5. Adhere to, abide by, as in I'm going to stand by what I said yesterday.
= erfüllen, festhalten
also auch: an der Mission (weiter) festhalten, diese erfolgreich fortsetzen
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Note added at 11 hrs (2008-04-10 01:49:37 GMT)
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typo corrr.: stä*r*ker...
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Note added at 11 hrs (2008-04-10 02:01:56 GMT)
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das "voll und ganz" kann die gewählten Verben noch verstärken.
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Note added at 11 hrs (2008-04-10 02:06:06 GMT)
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http://www.kitcoproducts.com/
Our Mission
Simple, our mission is to provide the highest quality fiberglass products for our customers so they can provide their products. We stand behind our quality made products with an unmatched guarantee.
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Note added at 14 hrs (2008-04-10 04:39:47 GMT)
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Couple of more things: first of all, I find the original phrasing rather "cautious" as if saying "yes, with the contract, they will certainly fulfill their mission" is too much of a promise.
Anyway, I think it depends on how strongly the client wants it to be worded. You can certainly just say "(voll und ganz) hinter ihrer Mission stehen/die Mission (wirkungsvoll/glaubhaft) vertreten" (as suggested) but to me, it's too wishy washy. But so is the original - except I did right away think of "fulfill the mission" because the maintenance contract is something very concrete with, hopefully, concrete results.
More native speaker input would also help you here.
Below is a summary of meanings of the phrase which in German pretty much confirms any of the suggested terms.
another choice for me would be:
(den Erfolg) ihrer XXX Mission sicherstellen/garantieren
http://onlinedictionary.datasegment.com/word/stand behind
stand behind - Moby Thesaurus II by Grady Ward, 1.0 :
34 Moby Thesaurus words for "stand behind":
assure, attest, back, back up, be sponsor for, bond, certify,
champion, confirm, countersecure, endorse, ensure, get behind,
get in behind, guarantee, guaranty, insure, run interference for,
second, secure, side with, sign, sign for, sponsor, stand back of,
stand by, stand up for, stick by, stick up for, subscribe to,
take sides with, undersign, underwrite, warrant
I think that's it ...for now:)
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The translation workplace 
peer agreement (net): +2
