Squeeze lime halves in citrus juicer to extract as much juice as possible. Transfer 3/4 cup lime juice to bowl; cover and chill. Reserve remaining juice for another use. Using scissors, cut out membranes from hollowed lime halves. Enclose lime cups in resealable plastic bag. Freeze until frozen, about 4 hours.
Mix orange juice, 3/4 cup lime juice, grenadine, salt, and cayenne in blender. Transfer mixture to pitcher. Cover sangrita and refrigerate until cold, about 2 hours. (Can be made 1 day ahead. Keep sangrita chilled. Keep lime cups frozen.)
Arrange frozen lime cups on serving tray. Pour sangrita into 12 lime cups; pour tequila into remaining 12 lime cups and serve immediately.
