Pour 3/4 cup water into pot. Add cranberries. Bring water to a simmer over medium heat. The cranberry skins may start to audibly POP as they crack. Once they begin to simmer, simmer 9 minutes, stirring occasionally. You may need to reduce the heat to medium-low to prevent boiling. Remove from the heat, so mixture can begin to cool.
When mixture is cooled to warm, pour into blender. Purée until smooth, about 35 to 45 seconds.
In small saucepan, place remaining 1 cup water. Sprinkle gelatin on top; or stir in agar-agar. Allow 2 minutes for the thickener to bloom (it will absorb the water and become translucent). It's okay if there's a tiny bit of gelatin left that isn't dissolved. For gelatin version, heat and stir over medium low heat until very steamy and dissolved but not yet simmering. For agar-agar version, bring to a simmer, stirring occasionally. Then simmer for 1 full minute.
Combine cranberry purée, gelatin mixture and sweetener of choice. Whisk or stir together well.
Dispense into molds of choice right away, so purée doesn't begin to thicken. (I like to use this glass baster, so I don't have to use the plastic ones.)
Chill for 3 hours minimum or overnight. To unmold more easily and neatly (especially with small detailed molds), place in the freezer for 30 minutes. Unmold, defrost slightly and serve or store.