The Blues face a trip to Guinness Premiership outfit Newcastle Falcons while the Scarlets travel to France to face big spending Toulon.
The Scarlets will face another French test after securing their place in the quarter-finals of the Amlin Challenge Cup this weekend with a win in Brive.
The Scarlets will play Toulon on the 8/9/10 of April in the Stade Felix-Mayol in the South of France against a strong French club with a great home record.
However, with the Scarlets' away results as successful as their home form in this season's Heineken Cup with two impressive wins as visitors against London Irish and Brive, Head Coach Nigel Davies said the team have a lot of belief.
He said, "It is going to be a challenge to go there, playing French teams in their home grounds is never easy and Toulon are a quality side and a big budget playing squad and some very good players - so it will be difficult.
"Saying that, our team has had great away experiences in this season's Heineken Cup campaign and so there will be a certain amount of belief within our group that we can get a result.
"We've just encountered what it can be like to play French sides at home and I'm sure, like Brive, there will be a passionate French crowd, plenty of exciting rugby and a team fiercely defending a strong home record."
The Scarlets were the first Welsh region to secure a win against Brive in Europe on Saturday afternoon.
He said: "Winning away from home is all about belief and the desire to win and that is what our group of players has shown both at London Irish and Brive, who also have good home records. The result on Saturday was great effort by the team - particularly the younger players who really stood up to the pressure Brive put on us.
"We are just delighted to be in the quarter-finals of a European competition and will be looking forward to the quater-final in April.
"From where we have come from in year one of our rebuilding process, to now be in a position where we are a couple of games away from a final in Europe is a massive achievement for this squad.
"We've come back from mid December with three back-to-back wins and I've been proud of how the boys have performed recently and are developing as a group."
And commenting on the move of the third, fourth and fifth best Heineken Cup pool runners-up into the latter stages of the Amlin competiton, Davies said:
"I think it's great for the profile of both the competitions and for the clubs involved because it adds to the season, with plenty to play for going forward. The Amlin Challenge Cup has had some good sides competing - with the likes of top placed Guinness Premiership teams like Saracens and Newcastle."
The qualifiers and their rankings for the Amlin Challenge Cup 2009/10 quarter-finals are:
1. Connacht Rugby (Top ranked AAC Pool winner)
2. Toulon (Second ranked AAC Pool winner)
3. London Wasps (Third ranked ACC Pool winner)
4. Newcastle Falcons (Fourth ranked ACC Pool winner)
5. Cardiff Blues (Third best Heineken Cup Pool runner-up)
6. Gloucester Rugby (Fourth best Heineken Cup Pool runner-up)
7. Scarlets (Fifth best Heineken Cup Pool runner-up)
8. Bourgoin (Fifth ranked ACC Pool winner)
The quarter-final matches, to be played 8 / 9 / 10 / 11 April, 2010, will be:
1 Connacht Rugby (ACC 1) v Bourgoin 8 (ACC 5)
2 Toulon (ACC 2) v Scarlets 7 (Heineken Cup 3)
3 London Wasps (ACC 3) v Gloucester Rugby 6 (Heineken Cup 2)
4 Newcastle Falcons (ACC 4) v Cardiff Blues 5 (Heineken Cup 1)