For the pear-cardamom compote with lime, wash the pears, peel and cut into small wedges. Squeeze the lime, finely grind the cardamom seeds (best in a mortar).
Bring pear wedges, water, cardamom, sugar and lime juice to a boil in a large pot. Simmer the mixture for a good 10 minutes, stirring repeatedly with a wooden spoon.
Pour pear-cardamom compote with lime into dessert bowls and serve warm.