What are some techniques for making a surface reflective in OpenGL

I want to make a surface reflect stuff, like water does

I saw a neat technique that involved using a framebuffer object to get a texture of what's above the surface and then put that texture on the surface. This is overly simplified, but that's the gist of it.

My problem is that I'm using an fps-style camera. That technique seems to only work if the camera rotates around the centre of the surface. But, if I go and look at an object at the edge of the surface, that's going to be in the middle of the texture and the effect will be completely wrong.

So... yeah... Are there any techniques that would allow me to make a surface reflect stuff, given my choice of camera controls?