Coming through the first three rounds unscathed would not usually bring cheer to a player who has reached the final in his last three majors but Murray could be forgiven for giving himself a pat on the back this time around.
He has managed to navigate the rough seas that have shipwrecked a fleet of top seeds and can now look forward to calmer waters after a 6-2 6-4 7-5 win over 29th ranked Robredo.
With Roger Federer and Rafa Nadal among those strewn on the rocks, Russia's Mikhail Youzhny, seeded 20, is the highest ranked player blocking Murray's path to a likely showdown with top seed Novak Djokovic in the showpiece match.
As if the hopes of a nation looking for a British man to end a 77-year barren run at Wimbledon were not enough of a millstone for Murray to carry, there is now the added weight of him being expected to at least reach the final.
"I think there's a lot more pressure on me now with them being out," he said. "There are papers in the locker room, so you see some of the headlines. It's not that helpful.
"You need to be professional enough to not let that stuff bother you and just concentrate on each match."
The home fans' hopes, however, are built on the solid foundation of recent results.
Murray has been among the most consistent performers at the Grand Slams, only failing to reach the semi-finals once since the US Open in 2010.
Added to that record, is that fact that he has moved slickly past three opponents without dropping a set.
Although no prizes are awarded for hitting top form in the third round, the number two seed can be satisfied with the way he outplayed Robredo with his aggressive ball striking.
He broke for the first time in the third game of the first set against the number 32 seed and followed that with two more to close out the opener.
A rasping backhand pass delivered another break at the start of the second set and, apart from a brief moment of vulnerability as he was serving it out, the Scot never looked like relinquishing control.
The 31-year-old Robredo, who had never been past the third round in 12 appearances at Wimbledon, upped his aggression levels in the third set but found Murray's defences watertight.
The home favourite broke in the 11th game and wrapped up the win when Robredo netted a backhand on his second match point.
The wet weather, so often an accompaniment to proceedings at SW19, meant the match was played out entirely under the Centre Court roof.
It was the first time Murray had played under cover at the grasscourt slam since losing last year's final to Federer. Then the change in conditions was widely said to have contributed to his downfall.
It should come as no surprise, therefore, that he told reporters he prefers being exposed to the elements.
Waiting for Murray in the last 16 will be the winner of the match between Youzhny and Serbia's Viktor Troicki, which was kept off court by the persistent rain that dogged the day.
Round 3 results
2-Andy Murray (Britain) beat 32-Tommy Robredo (Spain) 6-2 6-4 7-5
24-Jerzy Janowicz (Poland) beat 15-Nicolas Almagro (Spain) 7-6(6) 6-3 6-4
Jurgen Melzer (Austria) beat Sergiy Stakhovsky (Ukraine) 6-2 2-6 7-5 6-3
Adrian Mannarino (France) beat Dustin Brown (Germany) 6-4 6-2 7-5
Round 2 results
4-David Ferrer (Spain) beat Roberto Bautista (Spain) 6-3 3-6 7-6(4) 7-5
13-Tommy Haas (Germany) beat Jimmy Wang (Taiwan) 6-3 6-2 7-5
28-Jeremy Chardy (France) beat Jan-Lennard Struff (Germany) 6-2 5-7 7-6(6) 7-6(4)
26-Alexandr Dolgopolov (Ukraine) beat Santiago Giraldo (Colombia) 6-4 7-5 6-3
Grega Zemlja (Slovenia) beat 29-Grigor Dimitrov (Bulgaria) 3-6 7-6(4) 3-6 6-4 11-9
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