1. Remove the peel from 2 of the grapefruits with a paring knife by lopping off the round ends and slicing off the skin and the white pith. They don’t have to look perfect and if some of the white pith remains, it’s not a problem. Use the knife to cut the grapefruit sections out, away from the membranes. Put the grapefruit sections in a large nonreactive pot and squeeze the juice from the membranes into the pot as well. (You can reserve the grapefruit skin pieces for another project, such as candying.)
2. Slice the remaining two grapefruit rinds in half crosswise and juice them, adding the juice to the pot. Use a soup spoon to scrape out the membranes and discard them.
3. Cut each juiced grapefruit half in half, so you have eight grapefruit quarters. Use a chef’s knife to cut the grapefruit rinds in quarters crossways (rather than lengthwise), then into strips about 1/4-inch (.75cm) wide. Add them to the pot, along with the water, sugar, and salt, and bring to a full boil. Turn the heat off, cover, and let stand 1 hour. (It can sit overnight.)
4. To finish the marmalade, if you have a candy thermometer, clip it to the side of the pot and bring the marmalade mixture to a boil, then reduce the heat so it’s at a low boil. If you don’t have a candy thermometer, either use a digital thermometer or follow the instructions in the next steps. Place a small plate in the freezer, to test the marmalade later.
5. Cook until the mixture is reduced by about half. Add the vermouth and continue cooking until the syrup around the grapefruit pieces is as thick as warm maple syrup and the bubbles are no longer foamy, but thick and transparent. The temperature should read about 215ºF (101ºC). Turn off the heat and place a bit of the marmalade on the chilled plate. Return it to the freezer for a few minutes and check it using the “wrinkle test;” if you nudge it with your finger and it wrinkles, it’s done. Marmalade generally sets at 218ºF (103ºC) but this one may set sooner.
6. If not, continue cooking and checking the marmalade, checking once or twice more, if necessary, until it’s done. (Make sure to turn the heat off under the marmalade while you’re cooling your samples to check since it’ll keep cooking, and may already be done.) Ladle the marmalade into clean jars with lids. If you’re not planning to eat it within a week or two, store it in the refrigerator, where it’ll keep for several months.