Place port in a small pot and bring to a boil over high heat. Reduce to a simmer and cook until you have ¼ cup remaining, about 30 minutes. Place in the refrigerator to cool.
While port reduction is cooling, make the mascarpone cream.
Using a stand mixer fitted with the whisk attachment, whisk the mascarpone cheese, sugar, vanilla extract, and salt on medium speed until well mixed, about 30 seconds.
Reduce the speed of the mixer to low and slowly stream the whipping cream. Once all of it is added, scrape down the sides of the bowl, and return the mixer to medium speed. Whisk until firm peaks form, about 1 minute. Place the cream into the refrigerator.
To grill the peaches, bring a grill pan or grill to medium-low heat. I you like, brush each peach half with the melted butter and place on the grill pan. Grill the peach halves until they are slightly softened and have dark grill marks, 6 to 8 minutes.
Allow the peaches to cool slightly, top the peaches with the mascarpone cream and drizzle with the port reduction.