Peel the shrimp and pack them into jars, leaving 1 inch of headspace.
Ladle the hot brine over the shrimp. If you're watching your salt intake, use boiling water and omit the salt.
Remove any air bubbles and add brine to maintain the 1-inch headspace.
Wipe each jar rim with a warm wet washcloth dipped in vinegar.
Place the lid and ring on each jar and hand tighten.
Add hot water to your pressure canner as per the manufacturer's requirements (often 3 quarts).
Place the hot jars in the pressure canner, lock the lid, and put the canner on high heat, bringing it to a boil.
Let the canner vent for 10 minutes, then close the vent and continue heating to achieve 11 PSI for a dial gauge and 10 PSI for a weighted gauge, or according to your elevation.
Process both pints and half-pints for 45 minutes.
Once the canner is at zero PSI, remove the lid, deflecting the steam away from your face.
Allow the canner to sit undisturbed for 10 minutes before removing the jars from the canner.
Place the jars on a cutting board and allow them to cool undisturbed for at least 8 hours or overnight.
Once all the lids have been sealed and the jars have fully cooled, remove the rings and wash the jars in warm soapy water.
Store the rings to reuse, then label each jar with the name and date before storing.