Emery trusts keeper Olsen for Aston Villa's Europa Conference League semi-final
World Cup winner Martinez will miss the match at Villa Park after picking up three yellow cards in the competition so far, with two of those coming in the second leg of the quarter-final in Lille.
The Argentina goalkeeper starred in a drama-filled penalty shootout last month, saving two spot-kicks and displaying his trademark dark arts.
Olsen may well have been playing anyway as Martinez sustained a hamstring injury in the first half of Saturday's 2-2 draw with Chelsea, with the 34-year-old coming on at half-time.
He conceded two goals, but also made a vital save at the death to deny Cole Palmer and earn his side a point.
Emery said at his pre-match press conference on Wednesday that he and his team had total trust in Olsen.
"Martinez is very competitive and very important and helped us a lot," said the Spaniard. "But when an issue like that, the yellow card, and a small injury as well, we have to protect, help and support and push another player in the squad.
"Robin Olsen has been very competitive every day in training. When he played he helped the team and the team believes in him and trusts in his performances."
Emery did not say when he expected Martinez to return, with Youri Tielemans and Alex Moreno also sidelined. However, Nicolo Zaniolo could be fit after missing the past two games.
Villa are aiming to win their first European trophy since 1982 but are balancing that with a quest to qualify for the Champions League.
They are fourth in the table, seven points clear of Tottenham, who have two games in hand.
Emery conceded that the Premier League remains his priority, but not at the expense of trying to progress to the final.
"No way, he said. "The most successful teams in the world and my reference as a coach are the winning teams, Real Madrid, Barcelona, Liverpool, Man City, they're a guide for myself when I'm trying to play in different competitions.
"Now we are very excited with the Conference League and very motivated with the Premier League. It's not changing my first message when we started the season.
"The most important thing is the Premier League, then FA Cup and Carabao (League) Cup and Conference League and in case we're getting to the end of the season and being a contender then of course the importance changes a little bit.
"The first priority is still the Premier League but we're going to play both trying to do the best in both."