Of all the overused, misogynist cliches, damsels in distress (or DID’s) probably get the most eye rolls. “Oh, the love interest has been captured by the villain and needs to be rescued by her 
superhero boyfriend. What else is new?”
But! It doesn’t have to be this way.
The reason fans and feminists don’t like the DID is because the laziest version of it is the most popular. This is the one where the ditzy airhead with a big chest makes a stupid decision and needs to be rescued by the hero. Or, on the flip side, the highly trained, super competent assassin/robot/genetically modified soldier/whatever suddenly acts out of character or the established rules of world warp to make it so she’s in distress and she has to be rescued by the hero. Basically, the author breaks their own rules to make her a DID, usually for shipping fodder.
I don’t mind when a character—woman or otherwise—is in distress and needs to be rescued. The parts where so many authors fumble is how and why the DID is in distress, and also, how does the character react to this situation.
Let’s start from the top. You want to distress your character. How do you do this? Well, you put them in a situation that they cannot possibly escape otherwise. For non-combat characters, this is pretty easy. Jasmine from Aladdin and Danaerys Targaryen from Game of Thrones are not fighters, so once you get past the legions of guards it’s simple for them to end up as a hostage or prisoner.
For a character with combat capabilities, it’s a little harder to put them in a situation that your audience will genuinely believe they cannot escape on their own. But it can be done. In Avatar: the Last Airbender, there are several characters with very powerful abilities, but you take away access to their powers (especially for the earth- and waterbenders), and they’re straight-up stuck. In The Dark Knight Rises, Batman had to have his back broken by Bane and then get shoved down a hole for five months to recover.
Just grabbing a character’s arm isn’t going to work. So many times writers come up with an amazingly badass character only for them to be damseled in the worst ways. In Guardians of the Galaxy, Gamora has to be rescued twice. The second time (when her ship got busted and she was jettisoned into space) is fine, but the first instance I had issue with. She gets cornered by Drax and a handful of prisoners and needs to be rescued by Quill. Which is stupid, because she’s established as an amazing fighter. It would have made more sense for Quill to need rescuing—maybe someone he double-crossed in the past is also in that prison and is out for blood—and Gamora saves his life, forcing him to repay her by breaking them all out. And then Quill saves her during the space-jettisoned thing, and they’re one-for-one.
So, you’ve come up with a suitable enough threat for your DID. Now what do you do? Even if you have a dramatic rescue planned for the end, the DID probably doesn’t know that. Or they’re not willing to wait the twenty chapters it’ll take for them to get out. They need to have a realistic reaction to getting lost/kidnapped/held hostage/imprisoned.
Generally speaking, there are three types of reactions. The first is physically fighting. Try to pick the locks, try to knock out the guards, etc. Sometimes this works, sometimes it doesn’t. The point is, the character should at least try. This not only makes them more entertaining than a wet rag, 
but also establishes the power of the villain and/or seriousness of the situation when the DID can’t get out.
Second is play-along or manipulating. This is usually for characters who cannot fight physically but have other skills such as acting. Jasmine from Aladdin tries to seduce Jafar to distract him from Aladdin getting the lamp. It doesn’t work, but it’s a much more intense, entertaining scene than if she’d just sat on the floor and cried.
Third is no resistance. Yes, it is an option to not have your DID fight back against a terrible situation. But you need a damn good reason. In Toy Story, Buzz Lightyear is an established badass: smart(ish), charismatic, good fighter. But when everything he’s ever believed about himself and the world turns out to be nothing more than a story for children, he’s crushed. He doesn’t want to live anymore. He’s fine with being strapped to a rocket and blown to smithereens. It’s not until Woody convinces him that he can still have a fulfilling life as a toy that he starts fighting back.
There are a ton of possibilities here. Your damsel may know off the bat that they can’t win a physical fight, so they try to manipulate one of the evil minions into busting them out. Or they pretend to be depressed and scared to lure the villain into a sense of false security before making a break for it (bonus points if your audience also believes they’re depressed/scared before the reveal). Or they could fight their way through the evil lair just far enough to get a message to their friends before getting re-captured.
If you’re wondering whether or not your DID scene is any good, ask yourself these two questions:
1: Does it make sense for this character (especially if they’re an established badass) to be a damsel? If not, rework it or drop it entirely.
2: Is the damsel reacting to their situation in a realistic manner and using every ability they have to try to get out? If they’re rocking back and forth in a fetal position waiting for rescue, you’d better be equipped to defend yourself against the wrath of readers you’re about to incur.