Mike,

Two other pieces of information:

1) The dates of the tests are in column B, scores start in column C:DZ
2) The scores may be any number from 0 to 100 and not in any sorted order.  
The  highest score may not be the last score.

Maybe I just don't know how the LOOKUP function works, but with only 2
parameters, it's using the array form.  Won't the result be the highest score
not the last score?

Don, you are almost my hero.   This formula looks simple, but..... I probably
wasn't clear in my description

I can't seem to get this to work.  Probably because I don't understand how
array functions work.  Partly because I can't figure out anyway MAX will work
for this problem.  I believe I entered  it properly because I can see the
braces.

In your formula, I don't understand what you use H1 for?  The student names
are in rows 1 and 2 of each column, but I'm not looking for a name.  I'm
looking  for the last cell in the 14:61 range of each column that has
anything in it.  I'll put this formula in row 136 of each column.  This
formula will tell me the date of the last test score in the 14:61 range in
that column

The test dates are in B14:B61.  Only column B has dates in them.
The test scores are in the next 200 columns in the same rows as the dates.