My personal ruling would be to consider the armour as the cash on hand you have - it is not automatically converted to anything and you must still carry it around. The economy is not cash-based one. The armour counts as cash on hand in relevant interactions. I would allow it to count as a number of cash equal to half the obstacle of buying it, or at most the total obstacle (if it were in pristine shape, which is unlikely).
If you want to exchange it for actual physical coins or bank notes, then use the rules for generating cash on hand with your resources, with the armour as bonus cash on hand.
In either case, you need to have someone to sell the armour to - not a trivial task in most places for most characters. Circles rolls or similar are likely needed, unless you are playing nobles in a settlement with plenty of knights, or similar.
See also Burning wheel forums, for example: https://www.burningwheel.com/forum/showthread.php?11224-How-do-you-sell-things