A 20 Year tawny port is always appropriate with a cigar after dinner. But, it depends on your personal taste.
Depending on the lateness of the hour, the meal, and my companions, I might select a snifter of Benedictine and Brandy or Grand Marnier cognac...but, more likely, a glass of Cruzan Single Estate or Ron Zacapa Centenario Rum served with a splash of boiling water, to open the nose.
The sweet aperatif liquors the other SteveR recommends, above, would be far too sweet for me. Frangelico and Tia Maria are frequently used as ice cream toppings in upscale restaurants.