I live in the United States. I'd like to write a check to someone. I don't know the exact amount yet but I do know the upper bound. How can I write a check with no exact amount but with an upper bound?
The check is your commitment to pay to the order of the
payee the $
amount, signed by your hand.
Nothing else written on the check matters.
Your link refers to the NTE checks issued or received by the LA county, and the rules for these checks apply to the county itself, not the banks (source).