[jerf]

Since we're having a bit of fun, my suggestion would be to horizontally flip the level entirely. I suspect it would rapidly become more intuitive than you'd think; a shock the first couple of times, but just "how it works" after that.

Further edit: I have no idea why, but in my head the color palette shifts when the screen is reversed, like all the colors get 20% darker. (Perhaps I'm analogizing with A Link to the Past's "Dark World", which isn't really the same thing, but you are welcome to explain that to my subconscious at your leisure.) It doesn't seem like there's a good reason for that from a Portal point of view, but it would offer a subtle hint that you're supposed to be going the other way now.

[pak]

You wouldn't need to change the color palette. Freeze the gameplay and animate the world "flipping over" as a big 3D surface, like in Paper Mario. Continuity is established, problem solved.

[MikeCapone]

Would you have the controls also be reversed (left becomes right and vice versa)? I'm not sure what makes most sense. Maybe you'd get used to it after a while.

[Stabyourself]

What I am planning to do is make it like in games that have fixed cameras: When the camera changes, the character keeps walking into the same direction unless the player presses in another direction.

[jerf]

No, just the one. You step the portal and the only the world reverses. You keep holding right, and you go right-original, through the portal, then right-mirrored, but it's always right, so there's always agreement between the user's direction and the motion of Mario. It's the world that gets flipped instead of your control scheme.

The idea that Stabyourself puts forth is arguably the default answer, in the sense that it is the usual one, but while basically functional, it never ever feels right. I just got done with Catherine recently which does the same basic thing (albeit with going behind something instead of going through a portal, but it's the same reversal problem) and 18 hours into the game it still felt unnatural... and that's hardly the first time I've encountered the "keep going a certain direction while held, then completely rekajigger the interface at an arbitrary point in the future when the user recenters the controls", either, so it's felt unnatural for even longer than that. (For bonus points, play on an Atari 2600 controller that just likes to cut out for a frame or two every so often, so the effect is that the game's controls appear to simply spontaneously revert.) Flipping the world would at least be changing things up.