Quarter the grapefruit and squeeze the juice over a measuring cup. Fill a cocktail shaker or screw-top jar with ice cubes (about 4 large or 6 to 8 smaller ones) and strain the grapefruit juice into the shaker, catching the pulp.

Halve the lime and squeeze the juice over the shaker using a lime press or by hand. Add the tequila and agave syrup, then tightly seal the shaker or jar and shake vigorously for 20 to 30 seconds.

Fill two glasses with ice cubes (3 to 5 each) and divide the Paloma cocktail between them. If using a screw-top jar, strain the cocktail through a sieve or hold back the ice cubes with the lid or a spoon. Garnish with a grapefruit or lime wedge, if desired.