Wash the fruit. Stem the mulberries and pit the cherries, if using.

Combine fruit, honey, and lemon juice in a small, non-reactive saucepan over medium-high heat. Bring to a boil, then lower heat to medium.

Cook, stirring frequently, until the jam sheets off of your spoon or spatula.

Remove pot from heat.

For refrigerator jam, funnel the mixture into a half-pint jar, then seal, cool to room temperature, and refrigerate.

To can, prepare a one-jar water bath canner such as an asparagus pot and one half-pint jar, ring, and lid for canning. Funnel the mixture into the jar, then wipe the rim and seal fingertip tight with lid and ring. Process in the boiling water bath for 10 minutes.