You can weigh something using methods other than a scale. For instance, you can use objects as a stand-in for weight standards. If you know the weight of a given object, it can replace the usual units of ounces and pounds. To calculate an ounce using quarters, you need only to know the weight of one quarter and do some simple arithmetic.
Determine the weight of a single quarter. According to the U.S. Mint, one quarter weighs 0.2 oz., the equivalent of 5.67 g.
Divide an ounce by 0.2 oz. to get 5.
Stack or set aside five quarters to approximate 1 oz. in quarter weight.