The competition, which was part of the county's Year in the Orchard project, attracted 14 entries. The 8ha Whitethorn Farm was established in 2004 and is run by Martin and Rachel Soble.
A wide range of top fruit is grown, including gages, cherries, quinces and medlars, as well as traditional varieties of apples, soft fruit and vegetables, all sold locally and from the on-site farm shop.
Commenting on winning the two RHS awards, Martin Soble said: "The judges liked the combination of our traditional varieties and methods with our commercial approach to running the business."
The award event was hosted by RHS president Elizabeth Banks, patron of the Year in the Orchard and a Herefordshire native. She said: "Now is the time for the RHS to acknowledge and promote our unique orchard heritage before more is lost."
The Pomona Award is named after the Roman goddess of apples.