What I do is I prepare a front cap. It is a quad that fills the space that is not covered by a clipped portal.
The way I do that is that I calculate a line that is the result of portal clipping the near plane. This gives me a line in 2D. Then I find a point on that line that is closest to the centre (that will be a point that lies on a line perpendicular to the line we've just found, and it goes through 0,0, this makes it a lot easier, and we use that perpendicular dir anyway when constructing the quad). With that point, I am able to construct a quad. One important thing is that I make it a bit wider to cover any artefacts. Only a very little bit wider. I use a constant (0.0001f). I was experimenting with relying on near plane dist and other stuff and this constant turned out to work the best.
When I render the portal, I first render the portal as usual and then I render front cap (with no depth checks - it's near plane, right? but there are usual stencil checks (equal to current stencil depth, I increase it by one). When closing the portal (after interior is drawn) I render it the same way (one important difference is that test for stencil is provided value has to be less than in the buffer and I replace the stencil buffer content). I used to have decrease there, I used to not extend the cap, I was also experimenting with not using near plane. There were lots of odd things happening, sometimes the whole thing disappearing, sometimes there were just very narrow lines that were not covered (you could see stuff behind the portal).