Combine ¼ cup of water with the honey and allspice berries in a small pot over medium-high heat; bring to a simmer. Cook, stirring, until the honey dissolves, about 4 minutes. Let the syrup cool completely, then pour through a fine-mesh sieve into a small jar with a tight-fitting lid. Discard allspice berries. Store syrup in the refrigerator for up to 1 week.