In a cocktail shaker, muddle the basil and blackberries with tequila until berries are completely broken down.
Add the Splenda and lime juice, then fill halfway with ice and shake well.
Around the rim of a glass run the lime wedge and coat with Splenda or salt. If you are watching your salt, or would like a sweeter drink, use Splenda instead. Pour margarita into the glass and garnish.