First, to clear up a potential misconception, the Metro does not open at 5am and close at midnight per se. The times approximately represent when the first trains leave the termini and a handful of other key stations in the morning, and when the last trains depart at night from the main transfer stations in the core. The first and last train of a particular line to serve a particular station can be found by browsing each station's page on the WMATA website (Rosslyn's last train to Wiehle-Reston is scheduled for 11:47pm). And the last train of the night is always scheduled to run to the end of the line— a Wiehle-Reston train is not going to turn into a pumpkin at East Falls Church just because it turns midnight.
A more serious concern is Metro's plummeting reliability over the last several years, especially on evenings and weekends. The Blue Line has been particularly affected, as service was already drastically reduced, and until April 2016 (estimated) it is impacted by damage from an equipment fire (granted, not as much as the Orange and Silver— this time around).
WMATA does attempt to coordinate the last trains, and they announce when the last service has departed from the core. The last trains of the night are often delayed while station managers corral stragglers off the platforms, so I'd say you have a good chance of making the connection. If you prefer peace of mind, you could also take the Yellow Line to L'Enfant and transfer to the Silver Line there. The trip would be much longer, but your fare would not change, and you would still have the option of getting off at Rosslyn (or Rosslyn or West Falls Church on the Orange Line) to get a cab for the final stretch.
You can expect taxis to be waiting near every suburban Metro station around the time of the last train, and there is a taxi stand at Rosslyn (there is a massive construction project underway, so I don't remember exactly where it is currently located, but it shouldn't be more than a block or two away, and there will be signs). But consider that Rosslyn is only a few miles from the airport— a 5-minute drive at that time of night. As such, you don't really save any money by bothering with the train only as far as Rosslyn, so if you want peace of mind and have the financial wherewithal, you could simply take a cab from the airport. There is a $3 airport surcharge, but your Metro fare to Rosslyn is $1.90 anyway.
FWIW, Uber and Lyft are now legal in Virginia as well.