Figured it out after searching a little while longer, typical that I just made the question on this site.
Java code (I'm using LWJGL):
DoubleBuffer eqn1 = BufferUtils.createDoubleBuffer(8).put(new double[] {-1, 0, 0, 100});
eqn1.flip();
GL11.glClipPlane(GL11.GL_CLIP_PLANE0, eqn1);
GL11.glEnable(GL11.GL_CLIP_PLANE0);
As usual OpenGL is badly (as in poorly, not easy to grasp) documented and I had to search around until finally I found some that explained this on some forum (and revealed that the buffer must be flipped): The first three doubles are the normal of the clipping plane, the last (100) is how far from world's origin (0,0,0) the plane is.
So, if the camera is looking straight at (0,0,0) this example code above will create a plane on the right side that makes OpenGL not render stuff to the right of it. The plane is located on x=100 and is facing to the left (-1).
I hope this will be the search result for people looking for the answer to this in the future.