In a large pitcher, stir together the lime juice, sugar and 3/4 cup water until the sugar has dissolved. Add the tequila, Cointreau and blood orange juice. Cover and refrigerate until chilled, about 1 hour.
Moisten the rims of three 6-ounce martini glasses with the cut side of a lime half. Spread coarse salt on a small plate, then upend the glasses into the salt to crust the rims. Fill a cocktail shaker about 3/4 full of ice and measure in 1 1/2 cups of the margarita for 3 drinks. Cover and shake for about 15 seconds to thoroughly chill the mixture. Strain into the prepared glasses and hand to your guests. When you’re ready, finish the remaining margaritas in the same way.