Start by rimming your cocktail glass. Sprinkle a little salt on a small plate. Moisten the rim of the glass with lime juice or water, and dip the rim in the salt.
In a cocktail shaker, gently muddle the basil leaves. Add the blood orange juice, lime juice, tequila, and a few ice cubes to the shaker. Shake vigorously.
Strain the margarita into the rimmed glass with ice. Garnish with fresh basil and blood orange rounds if you're feeling fancy.