Your nihil promittere is correct, but let me explore some alternatives.
There are a number of choices to make.
The first one is choosing a verb.
The options that come to mind are polliceri, promittere, and spondere.
Your choice promittere has the issue of having several different meanings, and it can be misconstrued in a motto.
It seems to me that spondere is for more solemn promises than polliceri, and perhaps a coat of arms calls for some amount of solemnity.
I would therefore suggest spondere, but the choice is yours.
Check the links for details on these three verbs, or check any resource on our list of online Latin dictionaries for more options.
I chose to use numquam ("never"), but you can easily replace it with nihil ("nothing") if you prefer.
Also combinations are possible; ask for details if something specific sounds interesting.
The last choice is choosing a structure.
Using spondere, I might suggest one of these:
To never promise
One/Ones who never promises/promise
(This is really a participle, so the translation is not entirely accurate.)
We never promise
Never promise (as an order)
The first one might be most suitable, but I find the second one attractive as well.