The South African rider sits 13th overall, 34 seconds off Chris Froome's lead after days of racing and two difficult stages in the Pyrenees.
Meintjes switched teams at the start of the year, moving from MTN to Lampre Merida. The transition appeared relatively smooth but the 24-year-old found results hard to come but until the Dauphine, where he finished ninth overall. At the Tour he has looked composed in the mountains and there was a sense of relief emanating from him.
"At the start of the year I was feeling good and the shape was never really bad but I just didn't have anything to show for it so to come and ride like this is really satisfying. I've got to take the opportunities and see what comes," he told Cyclingnews.
"Sometimes you put in months and months of work and you have nothing to show for it, so it's nice to be able to show what I can do now."
On the stage to Luchon, Meintjes stayed with the GC contenders but could only watch on as stage winner and new race leader, Froome, attacked on the final descent.
"I just wanted to stay with the favourites today and then if I had the legs I was going to try something but today I was just hanging on for the last climb," he said.
"It was a fast pace all day but I'm happy with the legs and the performance in general. Hopefully I can feel the same to Andorra. I'm happy that nothing has gone wrong and that I'm getting the opportunity to show what I can do."
Meintjes also sits second in the young riders' classification, 18 seconds off Adam Yates's lead. The hunt for a stage also remains a target but Meintjes is aware that his stage ambitions and those on GC need to be carefully managed.
"It's really hard because the GC and the other riders really predict how the race will go, rather than the profiles. It's hard to look at advance and pick a stage. You need to base it on what happens in the day, what happened the day before and other factors.