Add tea and tarragon to a small saucepan and bring to a simmer on medium heat. Remove from heat and steep for 10 minutes. Strain into a heatproof container and cool thoroughly.

Combine watermelon and cucumber in a blender. Add lime juice and blend until smooth. Strain mixture through a fine mesh sieve into a pitcher. Add cayenne and stir.

Pour 1Ž2 cup tarragon tea and 1Ž2 cup watermelon mixture into each of 4 ice-filled glasses. Garnish each with a tarragon sprig.

Note: Step 1 can be made a day ahead and refrigerated. To make a cocktail, add a 1-ounce shot of tequila to each drink.