Cut the ends off the limes and upend on a cut side. Make 2 perpendicular slits lengthwise into the fruit to form an 'X', cutting only 3/4 of the way through. Pack lots of salt into the slits and place limes in a jar, pressing to compact and release juices.
Seal jar and let sit at room temperature for 12 hours.
Uncover limes and press firmly to compact. Repeat once or twice daily until limes are softened and submerged in juices, 2-3 days. If there is not enough juice to submerge limes after 3 days, add fresh lime juicec to cover.
Chill 1 month before using.