Loosing a Buddy: Do Turtles Mourn?

After the death of long-term companion, your 
little guy probably does miss his buddy. Turtles that live
with the same individuals for a long time seem to form some
attachment. So, he may miss her for a while (I am hesitant to call it
grieving, but...). However, I would't get him a
buddy since there is no telling how they'll get along.

I had a pair of Reeves turtles together for several years. 
I had to separate them when the male's advances became too rough.
The female seemed relieved to be rid of him. The male kept
looking for her for quite a while.

(I used to be very skeptical when people attributed human-like emotions
to turtles, but over the years I have learned that captive turtles do a
lot of things that we don't see in wild populations; and emotions, after
all,
are formed in the oldest parts of the brain. While turtles in the wild
don't seem to form special relationships, in captivity, if with the same
turtles/people for many years, they do.)