Combine sugar, water, and zest in a saucepan and bring to a boil.
Simmer for 30 seconds, then cool.
Add lime juice and bring to a boil again.
Remove from heat, stir in mint, and let cool.
Strain out the solids and bottle it up!
To serve: Mix 1 part cordial with 6 parts water (or more!) and enjoy chilled.