add player's position/angles into the portal view, so it does look like a whole into the other room (f.e.) not like a flat TV.
, the answer here is probably shaders. You may also try changing the VIEW's arc to 'warp' your flatscreen TV (perhaps also try aspect).
Changing arc etc won't really help in my situation (sure they will need to be tweaked at the end, but the problem is that I need to add camera's positions/angles on the top of the view positions/angles (the view, which is rendered on the texture of the portal). At least this is what I think I need to do, but I just can't get the math part