dnd 5e – How does concentration work when wild shape is ended through damage?

This is pretty simple, actually.

Whenever you take damage while
you are concentrating on a spell, you must make a
Constitution saving throw to maintain your concentration.
The DC equals 10 or half the damage you take,
whichever number is higher.

You make a Constitution saving throw “whenever you take damage”. So when you take 30 damage, you make a Constitution saving throw. Since you make this when you take the damage, you use the stats you have when you take the damage. So it will be a DC 15 Constitution saving throw which you make with a +5 bonus.

The same reasoning applies to the 60 damage case. So when you take 60 damage, you make a DC 30 Constitution saving throw using a +5 bonus. There is a caveat, though.

When
you
revert
to
your
normal
form,
you
return
to
the
number
of
hit
points
you
had
before
you
transformed.
However,
if
you
revert
as
a
result
of
dropping
to
0
hit
points,
any
excess
damage
carries
over
to
your
normal
form.
For
example,
if
you
take
10
damage
in
animal
form
and
have
only
1
hit
point
left,
you
revert
and
take
9
damage.

This suggests that the 30 carryover damage will count as being taken, so you’ll have to make another Constitution saving throw, this time at DC 15, using your own +0 modifier.