Bring water and salt to a boil, stirring until salt is dissolved. Let cool for 10 minutes, then pour over pitted sweet cherries. Cover and let sit 12 hours or overnight.
Drain cherries, discarding brine, and rinse in cold water. Set aside.
In a medium saucepan, combine sugar, water, lemon juice, and red food coloring. Bring just to a boil, stirring to dissolve sugar, and remove from heat. Pour over cherries, cover, and let stand for 24 hours.
Drain cherries, reserving juice. Set cherries aside. Bring reserved juice to a boil again. Remove from heat and stir in almond extract. Pour juice over cherries.
Pack cherries with juice in hot sterilized jars and seal according to manufacturer's recommendations. Place in a water bath canner and process 20 minutes for pint jars or 25 minutes for quart jars.