Don't publish anything related to your work-products, unless it's already available for everyone to see. Get a written permission from your employer so that you can include your pet projects in your portfolio as you like and if you're employer is in a good mood you can try to get a written statement which allows you to show images of specific private-work-related products (and if VERY happy you can even try to be allowed to show some code segments).
what are the reasonable limitations on that? Obviously, I don't own the product and can't claim to. But can I extract code segments and place them in a portfolio, or link to a project online that I worked on but don't own?
Not in any case are you allowed to publish source code of projects that your company owns and is developed during your office hours. But that doesn't mean you can't show what the products look like, if they're already available for everyone online. An exception to this statement would be if you'd get a written permission from your boss, stating that you're allowed to show a very specific subset of the code in your portfolio and or images of the private products, the latter is a more promising option.
According to my contract, anything I develop during the time I am employed belongs to the owner of the company, so even personal projects done off the clock cannot be used in a portfolio. Is there any move I can make that would be proactive towards developing a portfolio?
Ask your manager!
It's very unlikely that your employer has any interest in your small pet projects, just ask your manager whether it's okay or not for you to include your pet projects, that are not work-related at all, in your portfolio.
If (for any ridiculous reasons) they forbid you to publish the source code of your own projects, then at least ask for a written permission to show images of the projects in your portfolio. In the future you should try to avoid this in your contracts, but that's not always an option.
You can always take a chance and simply publish whatever you created in your spare time without asking anyone, it'll most likely not be noticed by your current employer and if it will then they'll probably not care, but getting a written statement from your current employer is the safe way if you want to be 100% sure.