I figured it out. [This post][1] was what I was looking for.
I needed to set my camera’s aspect ratio to 0.5625 which is an aspect ratio of 9:16 because of the portrait orientation.
http://i.imgur.com/v3n15st.png
This allows for the portrait view I was looking for, and it ensured that my background fit properly on each device I play it on without any clipping or distortion (assuming my background image is also 9:16, which it is). I hope someone else finds this helpful.
EDIT: While this answered my question it didn’t quite help me account for devices with aspect ratios that aren’t 9:16, such as the iPhone 4, and the iPad 2-4. Nearly all non-Apple devices are 9:16 when in portrait orientation. So I’ll need to come up with some way to scale the background when playing on Apple devices.