Venus Williams will meet her younger sister Serena in the semi-finals of the Sony Ericsson Open in Miami.

Venus Williams will meet her sister, Serena, in the semi-finals of the Sony Ericsson Open in Miami after a comfortable 6-1 6-4 win against Iveta Benesova.

Venus is gunning for her first title at Key Biscayne since 2001 and will go into the 20th All-Williams meeting full of confidence after casting aside her 26th-seeded Czech opponent in quick time.

By contrast Serena, the top seed, was far less convincing as she recovered from a set down, before also enduring a second-set tie-break, to eventually overcome the plucky challenge of Na Li 4-6 7-6 (7/1) 6-2.

The Chinese right-hander quickly established herself in the match by racing out to a 5-0 lead against a lethargic looking Serena.

The world number one eventually snapped out of her early malaise to grab back two breaks of serve, but she had given her opponent too great an advantage and Li finally served it out at the third time of asking.

If Li was expected to fade after her impressive start she did not read the script as she kept pace with Serena in the second set, and could even have taken a potentially decisive break at 4-4 only to fail to take her chance.

Serena was, however, clearly off her game and allowed her 27-year-old opponent another break opportunity at 5-5, which she also failed to take, before the set went to the tie-break.

Finally the world number one stamped her authority as she dropped just one point in the tie-break.

From there Li's hopes were undermined by an increasing error rate that allowed Serena off the hook as she claimed the decider 6-2.

Afterwards Serena, who is chasing a record sixth title in Miami, said: "[I] Definitely wasn't moving my feet at all (in the first set).

"I just wasn't doing anything that made a lot of sense at all. I'm a little disappointed. I don't think I played great, but I'm glad to have got through.

"I definitely played better in the third set, which was good. Because I needed to play pretty well to win the match."

Serena will now play her sister in the last four knowing she will need to improve.

She also must overcome a losing 10-9 career record against Venus and has lost three of their past four meetings, including last year's Wimbledon final.

In the men's event, Novak Djokovic battled a stomach complaint late on to beat Jo-Wilfried Tsonga 6-3 6-4 and book his place in the semi-finals.

The Serbian looked on course to end a four-match losing run against Tsonga, when he raced through the opening set before breaking in the fifth game of the second to go 3-2 ahead.

But two games later the world number three's problems became evident as he called a medical time out to help deal with stomach cramps.

After the break in play Djokovic was clearly still hampered as he missed 14 first serves and while it gave Tsonga a sniff of victory, the Serbian gritted his teeth to claim the match with a forehand winner down the line.

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Djokovic will now face Roger Federer in the semi-final after the former world number one won his late quarter-final against Andy Roddick 6-3 4-6 6-4.

Federer, who lost to Roddick at this stage in the event last season but who has a good track record against the American, is hoping to win his first title of 2009 at the event in Miami.

He had little trouble in picking up the first set after breaking Roddick's serve in the fifth game to take a 3-2 lead then doing it again to win the set.

But Roddick fought back in the second to win just his ninth set against Federer, before both players tested each other in the third.

Neither player could break the other's serve until the final game of the set when, with Roddick serving, Federer fought back from 40-15 to take the game to deuce, then got a lucky clip off the top of the net to go to match point.

The men's quarter-finals conclude tomorrow when Rafael Nadal faces sixth-seeded Argentinian Juan Martin del Potro, and fourth-seeded Andy Murray battles eighth-seeded Spaniard Fernando Verdasco.