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.
Notes
If you have a sweet tooth, add a drizzle of honey or agave to your cocktail before shaking.