Bring 1 cup balsamic vinegar to a boil over medium-high heat in a one-quart saucepan. Reduce the heat to medium or medium low, so the vinegar stays at a simmer. Simmer for about 15 minutes or until the vinegar is reduced by half.
Add the honey and stir to combine. Continue simmering until the glaze has thickened slightly. You will see that the bubbles take longer to pop, and the surface of the liquid seems to have more tension. By this time, the vinegar will be reduced to about 1/3 cup. This takes about 10 additional minutes after adding the honey.
Allow the glaze to cool, and pour into a small jar or squeeze bottle. Store in the refrigerator.