While Caribbean pirates had their Bombo (rum, sugar, and spices), British Navy sailors had Grog, flavoring their daily rations of rum with local citrus and sugar.
To be truly traditional, you’d make Grog with a dark or black blended rum (and maybe a little brackish water mixed in). We like this recipe from Smuggler’s Cove, which recommends an aged rum for a more refined flavor.
Note that this is a fairly sweet drink; some may wish to reduce the sweetener a bit.