In a large skillet over medium-high heat, combine raspberries and butter. Stir constantly until just boiling. Add sugar and honey and bring back to a boil. Continue to boil 3 to 5 minutes, stirring. Carefully pour mixture into medium bowl in ice bath. Stir several minutes. As jam cools, continue to stir from time to time. When cool enough to touch, add chopped basil.
Transfer to clean jars or plastic containers and refrigerate at least 1 hour. Serve on toast, in tart shells, or dollop on pound cake. Can be stored in the refrigerator up to 1 week.