Combine the lime juice, lemon juice, water, sugar, lime zest, and lemon zest in a small saucepan over medium heat. Bring to a boil, stirring, and cook until the sugar dissolves. Remove from the heat. Cool to room temperature.

Combine the cooled citrus syrup with the tequila and triple sec and chill thoroughly.

Meanwhile, chill margarita glasses and then wet the rim of each with a lime slice. Put the salt in a saucer and dip the rims into the salt.

Serve the chilled margarita mixture in salted glasses, over ice if desired, garnished with lime slices.