Sort and wash mayhaws. Cover 1 gallon of fruit with 3 quarts water.
Bring to a boil, cover and cook gently about 30 minutes. Drain through a colander, then strain through damp cheesecloth or a jelly bag; leave sediment behind.
Sterilize jars. Heat strained juice to simmering or at least 180°F and fill hot jars with 1/4-inch headspace.
Process pints or quarts 10 minutes at 0–1,000 ft, 15 minutes at 1,001–6,000 ft, or 20 minutes above 6,000 ft.