Combine the sugar, salt, and water in a medium-sized saucepan. Stir to dissolve the sugar and salt. Place the saucepan over medium-high heat and bring the mixture to a boil.
Once the mixture is boiling, reduce the heat to medium-low and let it simmer for approximately 5 minutes. This will create a simple syrup.
Add the raw cranberries to the simmering syrup. Stir to coat the cranberries with the syrup.
Continue to cook the cranberries for about 5 minutes or until most cranberry skins burst.
Remove the saucepan from the heat and carefully transfer the cranberry mixture to a heatproof bowl. Let it cool for a few minutes.
Stir in the orange marmalade, lemon juice, and Amaretto. Mix well to combine all the ingredients.
Allow the cranberry sauce to cool to room temperature. As it cools, it will thicken naturally.
Transfer the Amaretto cranberry sauce to a serving dish once cooled. You can refrigerate it until you're ready to serve. The flavors will meld together and intensify as it chills.
Keeps 1 to 2 weeks in the refrigerator or 2 to 3 months in the freezer.