In a large saucepan, combine the almond milk, rice, and salt and bring just to boiling over medium-high heat. Reduce to just simmering (low to medium-low heat); cover. Cook, stirring occasionally, for 12 to 15 minutes or until rice is soft but still has a bite to it. (Watch carefully, as the mixture does bubble up in the saucepan.)
Stir in the honey, cardamom, and cinnamon. Cover and simmer 10 minutes more or until the rice is very tender and most of the liquid has been absorbed (the mixture should be creamy). Stir in the cherries. Serve warm.