Select the edges on both halves then hit the L key to make a loop. Then go up to the menu and click Selection / Convert selection to points. Then use the average weld tool to connect the halves.
Only 2 caveats to expand on here:
1: The 2 halves must be welded into a single object first.
2: Be VERY CAREFUL with the “distance” adjustment. If adjacent points on either half are closer then the seams are to each other, you risk welding 4 or more points in places you only intended to weld 2.
One slick way way of minimizing or avoiding #2 is to add one step before average welding the points:
I made a sphere, cut it in half, and then mirrored it. Then I deliberately snaggled various points to exaggeratedly mimic problems commonly encountered while modeling half sections.
Then I selected the edges as per Ghostman’s method. Note the yellow arrow pointing at the “X size” parameter. This non-zero value indicates a deviation of some edge positions from a common vertical axis.
Set that value to zero and hit enter, and you get all the edges snapping perfectly aligned and vertical. (some details here that are usually no major problem but that you MIGHT want to check on with some models are that this method only assures vertical axis alignment. It does NOT assure that this vertical alignment is perfectly centered between the 2 halves (although it usually is), and it does NOT assure that point pairs are matched HORIZONTALLY)
From here you can convert edges to points and then average weld them.