There are console commands, if cheats mode is enabled:
This should work in both games. I believe you have to re-enter these every level, as you'll spawn in first person mode.
However, this will probably disable your ability to get Steam achievements for the games, so that's probably not the best idea. ModDB lists this mod for Portal 2, which should accomplish something similar. I haven't seen anything similar for the original Portal.
If you get vertigo, Portal games might not be for you - your perspective shifts frequently, and what's up is frequently down or sideways in rapid succession. The shift to third person might work OK in most other games, but you might find that Portal causes you more problems than other games.