I do software development and would like to run two Dell U2414H's in portrait mode as a single screen. Is this possible with a MBA 2013? Like this:
The MacBook Air will require a Dual-link DVI output using Mini DisplayPort to Dual-Link DVI Adapter to connect to the two monitors (so the monitors need DVI cables/connectors) and as long as the combined resolution of the displays is no more than 2500 x 1600 then it will work as that is the max resolution of an external display with this Mac.
If the combined Max resolution of these displays is higher than 2500 x 1600 it may well support both but you won't get the maximum resolution out of the displays.