Begin by wrapping the frame in bubble wrap to protect the finish. Wrap the bubble wrap in and out around the sides of the frame and hold it in place with tape. If the frame has glass, wrap the entire frame in a large piece of bubble wrap.
Cut two pieces of the extra cardboard to the size of the wrapped frame with the utility knife and tape it to the front and back of the frame. This will provide extra protection in the event the box is punctured.
Place the wrapped frame into the box. The box should be a snug fit for the box. You may want to wait to acquire the box until you have the measurement of the wrapped frame. The snug fit will reduce the chance of damage from movement inside the box during shipment. Tape the box shut and seal the seams with tape.
Ship the package with your shipper of choice, making sure to purchase insurance to cover the value of the frame. Most shipments are delivered without incident but unfortunately mishaps do occur and you should have coverage just in case.