Place a sheet of aluminum foil in your freezer so you have a spot to chill your sugar-rimmed glasses.
Pour 2 tablespoons of sugar into a small, flat saucer. Halve 1 of the limes crosswise. Cut one half into slices and set aside for garnish.
Holding a glass upside down so lime juice doesn't run down the outside, rub the cut surface of one of the limes around the glass's rim. Immediately dip the glass into the saucer of sugar to coat the rim all the way around. Gently shake off any excess sugar and carefully place the glass upright into your freezer on the sheet of foil.
Repeat with the other 3 glasses using same lime half.
Juice the remaining limes and the lemons and set aside. You should have 6 to 8 tablespoons of the lime and lemon juice mixture.
If you'd like to add fine mint ribbons to your drinks, stack 4 to 6 mint leaves per serving, roll the leaves up like a cigar, and cut across the roll, slicing the mint into fine strips. Set these aside and with your hands, tear apart 5 or 6 mint sprigs and toss them into a cocktail shaker.
Pour in the lime and lemon juice, rum, and the remaining honey. Using a wooden spoon, muddle this together, crushing the mint leaves to release all that fragrant mint oil. Cap shaker and shake well.
Remove sugar-rimmed glasses out of the freezer toss a handful of ice into each glass. Strain the drinks from the cocktail shaker into the glasses. Divide the mint ribbons, if you like, among the four glasses, and top off each glass with a splash of club soda.
Garnish each with a slice of lime and sprig of mint. Finish with a splash of Ouzo.