Place a few small plates in the freezer. Stir berries, sugar, lemon juice, and salt in a large heavy stockpot. Bring to a boil, stirring to dissolve sugar and mashing lightly with a potato masher. Skim foam from surface. Cook, stirring more frequently as jam thickens, until it has the consistency of very loose jelly, 8 to 9 minutes. Remove from heat.
Remove a plate from freezer; drop a spoonful of jam on it. Return to freezer for 1 to 2 minutes; nudge edge of jam with a finger. It should hold its shape. If jam is too thin and spreads, return it to a boil, testing every minute, until done.
Strain about half of the jam; discard seeds. Return strained jam to pot. Return to a boil. Remove from heat. Spoon hot jam into hot sterilized jars; cover immediately with sterilized lids.
Jam can be refrigerated for up to one month.