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In a small saucepan, stir together the 1/2 cup pineapple juice and the sugar.
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Warm over medium-low heat, stirring, until the sugar is dissolved. Let cool completely. (You can cool this down fast by placing it over an ice bath.)
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In a blender, puree the cubed mango, remaining 2/3 cup pineapple juice, and the lime juice. (You should have approximately 1 2/3 cups).
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Pour a thin layer of salt on a small plate or saucer. Rub the rims of 4 (10-ounce) cocktail glasses with one of the lime slices and dip the rims of the glasses in the salt to coat.
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Fill the glasses half full of ice. Set aside. Then fill a cocktail shaker half full with ice. Add half the puree mixture and half the pineapple syrup, then the tequila.
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Shake until well chilled and then strain into 2 of the glasses.
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Add a slice of lime to each of the 2 glasses. Repeat with the remaining ingredients, and serve.
Tips for success:
- For an easy variation, muddle 1 tablespoon fresh cilantro in the bottom of each cup before adding ice and the shaken margarita. Use a cocktail stirrer to stir the ingredients together.
- For a less sweet margarita, use less of the pineapple syrup.
- Make sure that the mango is very ripe and fragrant for the best results.