Add the cucumbers to a large blender and puree until smooth and completely blended. Pour the juice through a fine mesh strainer and into a bowl or measuring cup to separate the pulp from the juice.
Add the cucumber juice, tequila, triple sec, lime juice, and agave nectar to a pitcher or glass. Stir to combine. Taste and add more sweetener if desired.
Run a lime wedge around the rim of a glass. Dip the edge of the glass in salt and fill halfway with ice.
Pour the cucumber margarita into the prepared glass and serve.
Notes
Make it spicy! If you're like me and love cocktails with a little spicy kick, I recommend muddling some fresh jalapeño slices in your glass or pitcher. Just gently press down on the sliced jalapeños a few times with a muddler or the back of a spoon to release the oils.
Add some mint. Muddle a few fresh mint leaves with the cucumber for an extra refreshing taste!
Make it slushy. Turn this into a frozen cucumber margarita by blending all ingredients with ice to make a frozen version.