Unfortunately, the answer to the question you ask is is no.
If a device or a website or anything that requests a password is limiting you to only 8 characters, then there is really nothing you can do to somehow increase that limit. It’s a hard-coded limitation of the software involved.
The real question then becomes: what do you do instead?
And that, in turn, depends on your application.
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Do the best you can with what you have
The simplest, and honestly the most common solution in a case like this is to do as good a job as you can with what you’re given.
So you’re limited to only 8 characters then the best you can do is to simply make the best possible password that you can that uses 8 characters.
So that brings us back to the usual litany of using random characters selected from upper and lower case alphabetic characters, numbers and special characters. There are several good password generators that will do a very nice job of generating you a random 8-character password. One good example would be GRC’s Perfect Passwords – just copy any 8 characters from the random passwords that it generates, and you’re good.
But you may not have to.
Router passwords
In a case of a router’s administrative login – the login you use access the administration interface for the router – you may not need to get that involved.
To be really honest, 99.9% of the security you need with a router you get by having any password that isn’t the default password.
There exists malware that simply knows the default passwords for a huge variety of routers, and that relies on people never having changed that password. When this kind of malware infects a machine it simply tries all the different router default password combinations that it knows about to see if maybe one of them will work.
If it does, of course, the malware can then do nasty things to the router – all because the owner left the default password.
When it comes to your router, unless it’s a publicly accessible router somewhere other than your home, I’d actually be ok with an easy to remember, simple password. But if there’s any doubt, go for the 8 character random one.
Regardless of which you use, you can use a tool like Lastpass or Roboform to remember it for you.
Different requirements for different situations
If you encounter this limitation in other situations … well, it really depends on the situation.
If this were my bank, for example, I’d be really, really upset and would probably choose not to use that bank or at least not use that bank’s online services. 8 characters just isn’t sufficient security any more for anything that’s online and particularly anything so sensitive as financial information.
I believe secure passwords today should be a minimum of 12 characters with 16 or even longer being much, much better.
If you encounter this same limitation elsewhere you’ll need to consider how important it is, and whether you’re willing to settle for the 8 character restriction. If so, make the best of it, as described above.
For the admin password for a router that’s on your own network I think you’ll actually be just fine with 8 characters.
Besides, short of replacing the router, 8 characters is all you’re going to get.
Some websites have a limit like this as well – what I wish is that in this case they would show on the screen that it is that long (e.g. “Password [ ] (1-8 characters)”)… there are so many times where I have tried using my formula for generating the password (each website has its own password, based on a formula I use based on the web address), got an error, and then requested a new password!
Fortunately, none of the websites like this are “critical”, although ironically one of the police information sites I use has this restriction, but they didn’t respond to an email I sent about it!