I usually find it convenient to use "" in formulas such as the
following:

=IF(B120,B12/C4,"")

The problem of course is that an error will be returned if the cell
left blank with "" is used in subsequent calculations. Is there an
alternative to using zero instead of "" that still makes it obvious
that the cell is intentionally left unpopulated but that does not
result in #VALUE# errors?

A key question is, "how is the subsequent calculation supposed to treat the
cell?" If you want the cell to be treated as zero, my advice is to have the
cell's formula evaluate to zero. If you don't want zero displayed there,
then use either custom formatting or conditional formatting or
Tools Options View (uncheck) Zero values
to make Excel display what you want.