The Group Chief Executive of the Welsh Rugby Union and Chairman David Pickering have both sent messages of congratulations to the victors.
Roger Lewis, said: "This is great for Welsh rugby as a whole and a huge feather in the cap of both teams. I know how hard the players, back room staff and management have worked to reach this stage of the competition and I am delighted for them and their fantastic supporters.
"Both teams played with a power, style and commitment which proves that we in Wales have plenty to offer the rugby world.
"I also know how hard the Llanelli Scarlets and the Newport Gwent Dragons have worked and they can hold their heads high with pride because we all know just how high the standards are now in this competition.
"For now I want to wish all the very best to the Blues and the Ospreys for the quarter-final encounters. We wish them well."
Chairman David Pickering added: "It was a joy to watch the brand of rugby which secured both the crucial victories over the weekend. The conditions were far from perfect, but both showed how their hard work off the park pays of when it counts.
"The games were a credit to rugby and were a great shop window for the game which will help build the growing support base here in Wales.
"The Llanelli Scarlets and the Newport Gwent Dragons gave their all in one of the toughest rugby competitions in the world and we all know they have the resolve and skill to get right back up there."