Dice half the pineapple, then finely chop the remainder in a food processor. Add the diced and crushed pineapple, lime rind and juice to a preserving pan, then cover and cook very gently for 10 minutes. Add the kiwi fruits and cook for 5 minutes, until the fruit has softened.
Pour in the sugar and heat gently, stirring from time to time, until dissolved. Bring to the boil, then boil rapidly until setting point is reached (10–20 minutes). Skim with a draining spoon or stir in butter if needed.
Ladle into warm, dry jars, filling to the very top. Cover with screw-top lids, or with waxed discs and cellophane tops secured with elastic bands. Label and leave to cool.
To serve, this conserve is lovely with toast and butter.