Mix the sea salt, apple cider vinegar, and water and bring to a boil. Simmer for 5 minutes. Remove the brine from the heat and allow it to cool slightly. Arrange the cucumbers upright in a container large enough to hold the brine. Place the dill sprigs in amongst the cucumbers in the jars. The cucumbers should be fitted tightly and should come within 1/2-inch of the top of the container.
Fill the container with the brine to the top and tap on a flat surface to remove any possible air bubbles.
The pickles will last for up to a few weeks.