The next day, prepare the canning equipment by washing the jars, lids, bands, and canning tools in hot soapy water and rinsing thoroughly. Set the lids and bands aside until you are ready to use them.
Place the jar rack into the pressure canner, and fill with water per your pressure canner manufacturer's instructions: Presto is 3 quarts, Mirro is 2 quarts, and All American is 2 to 3 inches.
Fill the jars halfway with hot water, and then place them on the rack in the canner. Bring the canner to a simmer for 10 minutes (180˚F). Keep hot until you are ready to fill them.
Remove the beef stock from the refrigerator and skim off the fat that has risen to the top. Discard excess fat.
Return the stock to a large pot and bring to a boil over medium-high heat.
Spread a kitchen towel on the counter. Use your jar lifter to remove a jar from the canner. Pour out the water (save it for washing dishes), and place the jar on the towel. Keep the remaining jars in the canner, so they stay hot.
Use the canning funnel and ladle and fill the jar with hot stock, leaving a 1-inch headspace at the top of the jar.
Swirl the bubble popper through the jar and wipe the rim. Center a lid on the jar, place the band over the lid, and screw it on until fingertip tight.
Use the jar lifter to place the jar back on the rack in the canner, and repeat with the rest of the jars until the canner is filled, or you run out of stock. If you have leftovers, store in the refrigerator or freeze for longer.
Place the lid on the canner and lock it. Leave the vent open, adjust the heat to medium-high, and bring the canner to a boil. Allow the pressure canner to vent steam for 10 minutes, then place the pressure regulator on top of the air vent, and watch the pressure rise.
Once the canner has reached the correct pressure (10 pounds for weighted gauge, and 11 pounds for dial gauge canners.), set a timer, and process pint jars for 20 minutes and quart jars for 25 minutes at altitudes of less than 1,000 ft.
Adjust the heat as needed to maintain a steady pressure, and adjust altitude if necessary (see chart below).
When processing time is complete, turn off the heat, and let the pressure canner cool down to 0 pressure on its own. Once the canner is depressurized, let the canner cool additional 10 minutes before removing the lid.
Spread a kitchen towel on the counter, unlock the cover, and remove it by tilting the lid away from you so that steam does not burn your face.
Allow another 10 minutes for the jars to adjust to the change in pressure. If jars are still boiling, let them sit in the canner for another 5 minutes, or until the boiling stops.
Use the jar lifter to lift jars carefully from canner and place on the towel. Keep the jars upright, and don't tighten bands or check the seals yet. Let the jars sit undisturbed for 12 to 24-hours to cool.
After 12 to 24-hours, check to be sure jar lids have sealed by pushing on the center. The lid should not pop up. If the lid flexes up and down when the center is pressed, it did not seal. Refrigerate the jar and use up within a few days, or transfer to a freezer container and freeze for up to 6 months.
Remove the ring bands, wash, label, date, and store in a cool, dark location (50 to 70 degrees F). Use within a year for the best quality. Yields about 8 pints or 4 quarts depending on how long you cooked the stock.