Put the cherries, sugar, and orange juice in a saucepan and add about half a cup of water. Bring to a boil and reduce heat. Simmer for about 15-20 minutes, until cherries are broken down and sauce is slightly thickened.
Mix the cornstarch with cold water and stir until cornstarch is dissolved. Add it to the sauce and boil until thickened. When the sauce coats the back of a spoon (it will thicken up in the fridge) turn off heat. Add a splash of Grand Marnier (a teaspoon or so) and let cool enough to taste. Add more Grand Marnier if necessary, being careful not to overpower the cherries.
Let cool completely, transfer to a jar or airtight container with a lid and store in the fridge for about a week.