Is there any way of changing the dimensions of portraits being displayed in game? For example, make the big sized pictures bigger than 110X170 pixels. Thanks!

A program like Faststone Image Viewer will make it bigger, but you will lose picture quality.
http://www.faststone.org/FSViewerDetail.htm

True dimensions of Joinable NPC portraits being displayed in game is 210 x 330.
You can use Near Infinity to recover them from the game files.

There are actually three separate portraits for each of them. There's the 38x60 one used on the right side of the screen, the 110x170 one seen in the records menu, and then a third 210x330 that's only used on the character creation screen for choosing a portrait. The large one isn't ever actually used for anything but character creation. That's why custom portraits only need the other two sizes.

As for your actual question, the size of the portrait area on the right side of the screen isn't actually hardcoded, and can be changed, but you'd need to make new image files for the UI to make it look good. However, I'm not sure if the portrait picture sizes are hard-coded or not. In any case, I don't know of any mod that will change that stuff for you.

If you just want the pictures for non-game purposes, you can dig out the slightly larger portraits out of the Portrait.bif file using an extractor, like parysm suggested. You can make them bigger with a variety of image editing software, but going "up" in size will always result in a loss of quality.

I'd guess that OP wants to make them bigger in-game as part of a UI enlargement since he's running it at a higher res than it was designed for (i.e. a modern res). I think it is hard coded in, I remember the game being very fussy about your custom portraits in terms of colour depth and so on, and had no concept of scaling the images to fit the frame.