Flights subject to Ground Delay Programs and Airspace Flow Programs are held on the ground, taking specified delays at their departure airports, to address capacity constraints at their arrival airports and regions of en route airspace, respectively. These ground holds, ranging from tens of minutes to a few hours, affect a large number of flights and can disrupt air traffic operations on a national scale. It is therefore of interest to minimize additional delays for such flights. This paper analyzes the magnitude and nature of additional delays experienced by flights subject to ground holding, utilizing historical flight operations data for five airports whose arrivals experienced the most pre-departure ground holding in 2015. At four of these airports, arrivals subject to ground holding incurred additional gate-arrival delays substantially larger (about two to three times on average) than for arrivals that were not subject to ground holding. These inequities in additional gate-arrival delays were caused primarily by taxi-out delays at the departure airports. Airborne delays were a secondary cause of these delay inequities, and there was a minor contribution from taxi-in delays. There were mixed trends in the role of gate-departure delays not caused by ground holding. Overall, these results motivate a recommendation to expedite surface movements at departure airports for those flights already delayed by ground holding.