The 36-year-old made more mistakes leading directly to goals than any other player in the Premier League last term, and his distribution in particular has come under scrutiny during the opening weeks of the new campaign.
The summer arrival of Bernd Leno - who has so far had to wait for his Premier League debut - has increased the competition for goalkeeping places at the Emirates Stadium, and Emery insists that he is happy with both players after Cech kept his first clean sheet of the season against Everton.
"I'm a little surprised because there have been a lot of questions over Cech," Emery told reporters after the win.
"In pre-season and also in the first (league) matches with us, he's played with good performances. Bernd Leno will also improve with us and learn about this competition here.
"Petr has big experience and big quality. He's started the season very well and we think he's giving us the performance we want. Today he showed us that he's very good and continuing to work hard with this spirit every day."
Sunday's 2-0 win over Everton was Cech's 202nd clean sheet in the Premier League - more than any other player in the competition's history.