Line the air fryer basket with foil to create a well large enough to contain the ham, ensuring it contains the juices.
In a small bowl, mix together the softened butter, minced garlic, fresh sage, fresh rosemary, and fresh thyme. Spread half of the garlic herb butter over the ham, and set aside the remaining half.
Place the ham into the foil "basket", cover with foil (preferably not touching the ham), and cook at 300 °F (150 °C) for 50 minutes.
Using pot holders, carefully remove the foil covering the ham and rub the remaining butter on top of the ham, allowing it to melt.
Cook the ham at 375 °F (190 °C) for another 10 minutes.
Serve warm immediately. Refrigerate any cooled, leftover ham in an airtight container for up to three days.