I watched Apollo 13 again the other day, and it is the very rare film where the engineers are heroes. The solve the problem with brains rather than brawn, they work the problem.
What other films can you think of where engineers are heroes, where engineering smarts save the day and even save lives? Other than the TV movie Longitude, none come to mind.
The Tommy Lee Jones movie Volcano kind of fits your description, but had plenty of action, as well.
Force 10 From Navarone did this with the dam scene, as well. They didn’t have enough explosives to just blow up the dam, so they had to set up a shock wave with the explosives they did have, that would reverberate around the reservoir and overstress the dam and tear it apart.
I don’t know about the actual engineering in accomplishing such a feat, but it’s what they did in the movie.
African Queen with Bogart?
Much of The Dam Busters is about the engineers who developed a “bouncing bomb” to blow up German dams
The Fighting Seabees, maybe?
Independence Day? weak, i know.
That’s what I came here to post.
ARMAGEDDON? You didn’t specify GOOD movies.
How about the ductwork guy Harry Tuttle from Brazil? 
The hero of the TV series Prison Break was a structural engineer. While he didn’t actually design any load-bearing columns over the course of the show, he generally used his mind - in particular his spectacular planning abilities - to get out of trouble (and usually into bigger trouble).
Hardy Kruger in the original Flight of the Phoenix, until Jimmy Stewart used the shotgun shell to clear the cylinder.
Executive Suite. Furniture factory engineer William Holden makes chairs while the other execs play musical chairs.
Not a movie but this was basically the whole idea behind the series MacGyver
Arguably, Stanley Goodspeed (Nicolas Cage) from The Rock.
Iron Man?
Primer has engineers as the main characters, if not actual heroes.
The recent Denzel Washington movie,* Unstoppable,* where Denzel’s character was a train engineer, comes to mind.
The Australian movie The Dish may qualify, although it’s more of pseudo-documentary/dramatization than a movie with heroes/villains, and it’s not just engineers involved - technicians are at least as important.
Technically, in Independence Day it was the team that wrote the virus Jeff Goldblum delivered (or maybe he wrote it himself, but either way it’s the same) that saved mankind from the aliens. The credit can be spread around to Will Smith and Randy Quaid, plus POTUS in a jet fighter for making it succeed.
MacGyver.
Enigma set in Bletchley Park during WWI, where the hero is kind of a straight Alan Turing without the stutter. Though he is a mathematician, he is also an engineer in that he seems to have been involved in designing the computer.
a beautiful mind? good will hunting?