Step 1Peel, halve and core the pears.
Step 2Place the water, sugar, Port, cinnamon and star anise in a saucepan. Bring to a boil, then reduce heat to a simmer. Add the pears and simmer until very soft, about 10 to 15 minutes. Place in a bowl, cover and chill.
Step 1Using a mortar and pestle or a fork or potato masher, muddle the poached pears to make a puree.
Step 2Combine the pears, vodka, maple syrup, honey, lemon juice and lime juice in a large liquid measuring cup and stir to blend.
Step 3Fill a martini shaker with chipped ice. Add the pear-vodka mixture and shake (work in batches if necessary).
Step 4Strain the chilled pear-vodka mixture into 6 chilled martini glasses, filling them three-fourths full.
Step 5Top each of the 6 glasses with about 2 ounces of Champagne. Garnish each with a star anise and serve.