Place 1/2 cups water and sugar in a 1 qt saucepan.
Stir to combine well, and heat over medium high heat until boiling. Add the guava slices and lime halves, and lower to a simmer for 5 minutes. Line a glass pie plate with parchment paper. Using a slotted spoon, remove the guava slices from the hot syrup, and place on the parchment paper. Remove and discard the lime halves. Do not discard syrup.
Dry off any extra moisture from the guava slices using a paper towel. Place the pie plate in the freezer, and freeze the guava slices until ready to use, at least 1 hour in advance. Chill the reserved syrup in the refrigerator.
Pour about 1 oz of the chilled syrup in a champagne flute, and add a few slices of the frozen guava. Fill the glass with the chilled cava, and serve.