Squeeze the fresh limes and measure 1 1/2 cups of lime juice.
Add the tequila, lime juice, orange liqueur, agave syrup, and cold water to a large pitcher.
Stir thoroughly until combined.
Taste and adjust the sweetness with additional agave if necessary.
Cover and refrigerate for at least 1 hour.
Before serving, run lime wedges around the rims of the glasses and dip lightly into coarse salt.
Fill each glass with fresh ice.
Stir the chilled margarita mixture again and pour over the ice.
Garnish each glass with a fresh lime wedge and serve.