Add the saffron strands to warm water. Let it sit for 10 minutes. The liquid will turn a beautiful golden-orange. This step is what gives the drink its color and aroma, so do not skip it.
Roll the limes on the counter with the heel of your hand to soften them. This helps you extract more juice. Cut them in half and squeeze the juice through a strainer into a large jug. Discard the seeds and pulp.
Add sugar, black salt, and a pinch of regular salt to the jug. Pour in 1 cup of cold water and stir well until the sugar dissolves completely.
Pour in the bloomed saffron along with its soaking liquid. Add the remaining 3 cups of cold water and stir.
Take a small sip. Add more sugar if it tastes too sour, squeeze a little more lime if it feels flat, or a pinch more black salt if it lacks depth.
Fill tall glasses with 7-8 ice cubes. Pour the saffron nimbu pani over the ice. Garnish with fresh mint leaves and a thin slice of lime. Serve right away.