I just finished a point of sale signage gig in vertical orientation.
It's no big deal with modern software.
I use FCP X, so the first step was to create a project with a 1080x1920 tall native raster.
Then just zoom, crop, shoot or otherwise custom create your content to fit that frame.
It gets a bit tricky when it comes to output, cuz most screens are horizontal and if you just export as normal, you'll get large pillar boxes of black framing your output as seen above. That might fit your display or not.
In my case, the playback was going to be on large LCD screens rotated 90 degrees counter clockwise in the field, so when my edit was done, I just applied a 90 degree clockwise rotation to the whole thing before I exported the master file.
The key is talking to the client so you know the delivery specs going in.
Hope that helps.