Meaning
To vouch for someone / To trust completely
Example
Meu irmão é uma pessoa muito boa e honesta, por ele coloco a mão no fogo.
My brother is a very good and honest person, I vouch for him completely.
Origin
The expression goes back to the medieval trial by ordeal, the so-called "Judgment of God." An accused person had to grasp or carry a red-hot iron; days later the hand was inspected, and a clean, unburnt hand was read as proof that God had shielded the innocent.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity