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?
A possible expression is a gentleman’s agreement:
variants: or gentlemen’s agreement
: an agreement secured only by the honor of the participants
// That also ties into recent speculation that Chelsea have a gentleman’s agreement not to pursue Napoli players.
— SI.com, “Chelsea Submit ‘Important Offer’ for Juventus Defender as Summer Business Finally Gets Going,” 22 June 2018
These are sometimes legally enforceable, and sometimes not. It depends on the context.
In the age of knighthood and chivalry (at least according to its reputation in media and popular culture), honour was a much more significant commodity than it seems to be today. Assuming that was actually the case, then saying on my honour, especially where witnesses were involved, would have been almost as good as actually signing something.