In Brazilian Portuguese, we use the following expression:
Fio do bigode (mustache wire/thread or mustache hair)
Here's what I found after researching:
It consisted of a man giving as a warranty, for his word, a thread of his beard, usually removed from his mustache. Of controversial origin, mustache may have come from the old German expression pronounced in the oaths: "bi Gott", or "by God"
O contrato entre as duas partes foi firmado pelo fio do bigode.
Which Google Translate readily translates to:
The contract between the two parties was signed by the mustache.
The above expression means that both parties agreed to something without actually signing a written contract or equivalent. Basically, both parties trusted each other by the other's history/legacy/references/appearance/influence/promises or anything that might have transmitted confidence.
What would be an equivalent English expression?