Strain cherries over a bowl, reserving liquid. Slice half the cherries into quarters and set aside.
In a blender, purée remaining cherries with the reserved juice, then pour into a medium bowl. Whisk in cream, milk and sugar. Cover and chill 2 hours.
When ready to make the ice cream, add amaretto and mix well. Pour liquid into machine and freeze according to manufacturer’s instructions. In the last few minutes of churning, mix in the reserved sliced cherries. Scoop ice cream into freezer containers and chill completely, until ready to serve.