Peel gingerroot and slice thin; cut the slices into thin strips. Cook the gingerroot in a saucepan of simmering water for 10 minutes. Drain gingerroot and discard water.
In a saucepan large enough to hold pears lying on their sides, bring 9 cups water to boil with gingerroot, sugar, Port, and lemon juice, stirring until sugar is dissolved.
Peel pears, leaving stems intact, and cut a thin slice from bottom of each if necessary to enable pears to stand upright when served. Arrange pears on their sides in poaching liquid, adding water as necessary to just cover. Simmer pears, turning them occasionally, until tender, 20 to 40 minutes depending on ripeness. Carefully transfer pears with a slotted spoon to a bowl and boil poaching liquid until reduced and slightly syrupy.
In a small bowl, whisk together the mascarpone and orange zest.
Pour sauce over pears. Pears may be made 1 day ahead and cooled in sauce before being chilled, covered. Serve pears warm or chilled, with dollops of the mascarpone.