Certain example embodiments of this invention relate to vacuum insulating glass (VIG) units, and/or methods of making the same. More particularly, certain example embodiments relate to VIG units having large pump-out ports, and/or methods of making the same. In certain example embodiments, a vacuum insulating glass (VIG) unit is provided. First and second spaced-apart glass substrates are provided, and a gap is provided between the spaced-apart substrates. A pump-out port has a size (e.g., diameter) of at least about 30 mm. A cover seals the pump-out port. A getter is in communication with the gap. The pump-out port is sealed using the cover, in making the vacuum insulating glass unit, via a sealing material provided proximate to the cover and/or proximate to the pump-out port.