I've accidentally exposed two 400 ASA B&W films at 200 ASA. One I developed like a 400 and the negative has come out very under exposed. Any advice on how I can salvage the other one?
I've accidentally exposed two 400 ASA B&W films at 200 ASA
In other words, you've overexposed it by a stop. (See What is the relationship between ISO, aperture, and shutter speed? if you need a refresher on that.) The fix for this is called "pull processing" (the opposite of "push processing", which is used when you underexpose, treating the fill as one rated for a higher sensitivity.
In general, this isn't recommended, as it often reduces contrast and gives a "murky" overall look, but having done it, it's probably your best option. The information for your chemicals should give you recommended pull processing times.
The puzzlement, though, is that you say you developed the film as normal and it came out under exposed. This is surprising, because that's the reverse of what would be expected in this situation.