Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh
Euro semifinalists from 2009, the Netherlands will face either England or France in Enschede on August 3.
A fresh Barcelona signing who spent last season with Rosengard in the Swedish league, Martens opened the scoring on 33 minutes with a low free-kick after Miedema had tripped over Jessica Samuelsson just outside the box.
Miedema added a second in the 64th minute after Shanice van de Sanden had found her in front of goal with a cross following a superb run down the right flank.
"It was really a great match, it's a great achievement," said Dutch coach Sarina Wiegman.
Midfielder Jackie Groenen said the match was "really tough".
"We had to run a lot but we worked really hard, we worked as a team and we're really, really happy we made it to the semifinals," she said.
Looking at the semi-final opponents, Wiegman said she could not choose.
"They're both very strong again. For me it doesn't matter who we play, we have to play the best game we can to beat them."
The Dutch pushed for a goal from the start, reducing Sweden to counter-attacking as they sought to extend their perfect record from the tournament so far.
Skipper Sherida Spitse fired over from a free-kick on 14 minutes and, moments later, Sweden keeper Hedvig Lindahl spilled the ball after a corner but Miedema failed to tame it for a shot.
On the other side, Sweden sweeper Nilla Fischer headed just over the bar from a corner on 25 minutes.
Sweden created two good chances just after half-time but Fridolina Rolfo slammed her left-footer past the post and Stina Blackstenius blasted over.
But the Dutch continued to dominate the game, with Spitse missing from outside the box and Miedema heading over and then sending her low shot wide.
"We created a few chances but we didn't use them. We didn't utilise the flanks as much as we wanted to," said Sweden coach Pia Sundhage, who will quit after five years with the team.
Germany are due to take on Denmark in Saturday's second quarter-final, while Austria will face Spain and England take on France on Sunday.
Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh
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