I think it's simpler just to create a new image to paste the two halves into...
File->Open photo # 1
File->Open photo # 2
File->New and specify approximate size needed for end result (e.g. if each is 400x400, specify 800x400)
You can use Image->Image Properties, if needed, to check the image size, or just swag it and pick
a big enough size.
Now, copy & paste the two halves:
Photo 1 : Edit->Copy
New : Edit-Paste
Photo 2 : Edit->Copy
New : Edit->Paste
Optionally use the exacto-knife "Crop Tool" to cut any excess background surrounding the end result (click and stretch to get the rough size, the pull each edge into final position, and click in the middle to crop - try it and you'll see what I mean).
Now File->Save As on the new photo to save it to disk.
Once you're comfortable with this you may choose to not copy & paste all of a photo but rather just a rectangle around the coin itself. To do this use the  rectangle select tool to select the part
you want to copy, then copy & paste as before.
If you took the photos without using a stand, they are probably not both quite the same size, and you can use Image->Scale
Image on one of the photos to resize it to match the other one.
A useful tip if you're resizing is to scale
by percentage rather than to a fixed size (because you're only interested in the size of part
of the photo - the coin - not the entire photo):
Use the calipers/dividers tool to measure the size of the coin itself in one photo, then to measure the coin at the same place on the second photo. Say the obverse
is 400 pixels, but the reverse
is 300 pixels. Now use the windows calculator to divide these numbers : 300 / 400 = 0.75, so you can now scale
by 75% to get it to match the reverse
(or alternatively 400 / 300 = 1.33, then scale