I have a worksheet that is 61 columns wide and 21 rows
high. I would like to be able to highlight the entire Row
and Column, relative to the cell that is active (up and
down, left and right), within this grid. Can anyone
suggest anything, perhaps in conditional formatting, that
might achieve this task?

You know selection is generally something to be avoided, but I assume
you really want it. Conditional formatting is one cool way but it would
seem to be "expensive" to have to format every cell on the sheet. AAR
for any such matters the first step should always be to check with Chip:
http://search.freefind.com/find.html...atch+ALL+words

and John:
http://search.atomz.com/search/?sp-q...6ae-sp00000000

You may be particularly interested in this instead of selection:
http://www.cpearson.com/excel/banding.htm

Since this is the programming area one programming solution is
sCol = Mid(ActiveCell.Address, 2, InStr(2,ActiveCell.Address,"$") - 2)
sRow = ActiveCell.Row
Range(sCol & ":" & sCol & "," & sRow & ":" & sRow).Select

If you want to limit it to 61 columns etc. modify the following.
Range(sCol & "1:" & sCol & "65536" & ",A" & sRow & ":IV" & sRow).Select

sCol is awkward because I don't know a direct way to get the column
letter. Perhaps someone else can supply that.

An alternate solution may be available with EntireRow et al.
You might poke around .Resize but I believe it's only for a rectangle.