OK. that sounds good so far, but if I'm doing this in a looping context, and the next time around the loop, the values of @arrayB change, won't that change all of the references as well?

It depends on where @arrayB is declared.

my @arrayA;
my @arrayB;
while (...) {
   @arrayB = ...;
   push(@arrayA, \@arrayB);  # XXX
}
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my @arrayA;
my @arrayB;
while (...) {
   @arrayB = ...;
   push(@arrayA, [ @arrayB ]);  # Ok
}
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my @arrayA;
while (...) {
   my @arrayB = ...;
   push(@arrayA, \@arrayB);  # Ok
}
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my @arrayA;
while (...) {
   my @arrayB = ...;
   push(@arrayA, [ @arrayB ]);  # Needlessly creating 3rd array.
}
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Also, how could I save the anon array in your second example?

What does "save" mean? Copy? You already have a copy of the array in @arrayB.