In a small saucepan, combine the blueberries, erythritol, and water. Bring the mixture to a gentle boil over medium heat, stirring frequently to prevent sticking or burning.
Once the mixture starts to boil, reduce the heat to low and let it simmer uncovered, stirring occasionally. Cook for at least 10 minutes, until the berries start to burst and the compote thickens. Use a fork, wooden spoon, or masher to break up the berries as they soften, adjusting the texture to your liking. The compote will thicken further as it cools.
Remove the saucepan from heat when the compote reaches your preferred consistency. Let it cool to room temperature, which takes about 10-20 minutes, before serving or transferring to a storage container.