This might be a better question for interpersonal.SE.

@ZachLipton I tried, but it was closed as off-topic. Because this involves flights, I thought Travel SE more fitting?

@Greek-Area51Proposal It wouldn't really vary in any particular setting or locale, however. How would you decline when you are in your home country to such requests at, for example, the bank or the supermarket? If declining politely is not enough for the other person, and you care about that other person that much, the best solution may be just to fly airlines that provide pens to passengers to fill out those forms.

I have a really nice pen to use and I also carry a spare generic one for people to borrow. It doesn't answer your question but it avoids me feeling uncomfortable saying no.

@Itai You should make that into an answer because … it is: it’s a really good way of avoiding the situation entirely (and seems to be the only way of meeting both of OP’s requirements: refusal, and politeness). And it’s currently missing from the answers.

I'm voting to close this question as off-topic because it does not appear to be about traveling within the scope defined in the help center.

@Greek-Area51Proposal: You asked it on interpersonal and got answers and even accepted one of them. What more are you hoping to get from here?

Carry a couple of spare biros.

"Sorry, no, I do need it myself," and keep on writing, whatever bit of paper you have handy, but a nice notebook will do.

I would ask why your question was closed on the interpersonal SE meta site. I'm not sure why it was closed, but when one SE closes your question you shouldn't just re-ask it on an even more off-topic SE.

Say the pen has some personal values to you. Like: Its my dad's present for "some special thing" or made up story "sounds bit matching you". So they will think the pen means lot to you and respect your opinion/feelings.

Keep a spare pen with a lid for such occasions. Lend the pen, but keep the lid. They can't put the pen in their pocket without a lid, and you holding the lid will remind you that you're missing a pen.

The people at IPS seem rather trigger-happy to close flight-related questions. I had such a question closed there too.

Carry spare pens that have a promotional message of a business or activity you, or someone you know, are involved in and offer to let the borrower keep it. A tip to get a borrowed pen returned: use pens that have caps and hold on to the cap while the borrower uses the pen. It's a reminder to you and a deterrent to them to put it in their pocket.

@BlueRaja-DannyPflughoeft Please see travel.stackexchange.com/questions/115844/…

@Chris An IPS moderator deleted that question.

Aside from the fact that the OP tried posting on interpersonal.SE and was told to post it here, I'd suggest to re-open because there is a component of this that relates particularly to airline travel as opposed to while walking down the street, or in another public place. -->

--> That is, on a plane, the other passengers that would like to borrow your pen are very much "captive" and very restricted in physical movement and availability of access to other resources to obtain a pen, so finding a polite way to refuse to lend your pen is a whole other level, compared to almost any other situation where you can suggest many other ways a person can obtain a pen.