A different approach adapted from an article in Cook's Illustrated,  using lemon and lime, after steeping the zest in the fresh juice for four to twenty-four hours.

Fresh Margaritas

The longer the zest and juice mixture is allowed to steep, the more developed the citrus flavors in the finished margaritas. We recommend steeping for the full 24 hours, although the margaritas will still be great if the mixture is steeped only for the minimum 4 hours. If you're in a rush and need to serve margaritas immediately, omit the zest and skip the steeping process altogether.

4 teaspoons grated zest plus ½ cup juice from 2 to 3 medium limes
4 teaspoons grated zest plus ½ cup juice from 2 to 3 medium lemons
¼  cup superfine sugar
Pinch salt
2 cups crushed ice
1 cup 100 percent agave tequila, preferably reposado
1 cup Triple Sec
 

Divide 1 cup crushed ice between 4 or 6 Margarita or double old-fashioned glasses. Strain juice mixture into 1-quart pitcher or cocktail shaker. Add tequila, Triple Sec, and remaining crushed ice; stir or shake until thoroughly combined and chilled, 20 to 60 seconds. Strain into ice-filled glasses; serve immediately.

FRESH PINEAPPLE MARGARITAS
Peel and core 1 small, ripe pineapple (about 3½ pounds); cut half the pineapple into rough 2-inch chunks (reserve remaining half for another use). Puree in workbowl of food processor fitted with steel blade until smooth and foamy, about 1 minute. Follow recipe above for Fresh Margaritas, omitting zest and steeping process, reducing lemon and lime juices to ¼ cup each, and adding ½ cup pureed pineapple to juice mixture.

FRESH RASPBERRY MARGARITAS 

Follow recipe above for Fresh Margaritas, omitting zest and steeping process and pureeing 1 cup fresh raspberries, lime and lemon juices, sugar, and salt in workbowl of food processor fitted with steel blade until smooth. Strain mixture into pitcher or cocktail shaker; continue with recipe, reducing Triple Sec to ½ cup and adding ½ cup Chambord (or desired raspberry liqueur) to juice and tequila mixture in pitcher.
For strawberry margaritas, substitute an equal amount of hulled strawberries for the raspberries.

Notes from Cook’s Illustrated regarding Margarita ingredients

After trying various proportions of tequila, orange liqueur, and citrus, they found the best margaritas were made with equal parts of each of the three major ingredients.
A premium tequila called reposado, meaning rested, made with 100 percent blue agave (the plant from which tequila is distilled) and aged for 12 months or less, has a slightly mellow flavor which blends well with the other ingredients. Grand Marnier and Cointreau are delicious, but Cook’s recommends choosing Triple Sec for the orange flavored liqueur in mixed cocktails; it  has a lower alcohol content than either Grand Marnier or Cointreau and a more delicate flavor.
Margaritas are traditionally made with fresh-squeezed lime juice, but not surprisingly Cook’s various experiments led to a different approach -- steeping the zest (no white pith) from the lime and lemon in their juices. This results in a full citrus flavor without the bitterness the white pith would contribute, and the addition of a little sugar to the mix counters any harshness.