What you are seeing is not an exception or an error, it is a warning. A subtle difference perhaps, but the eval and die technique will not trap warnings.

What you need to do is to temporarily modify __WARN__ so that instead of the default, which is to print out the warning, it does what you want. You say that you want to catch the "error" and generate your own message. You could do something like this:

sub my_comparison{
  @_ == 2 or die "Incorrect number of args to my_comparison";
  local $SIG{__WARN__} = sub { print "Tried to test a non-number with 
+==\n" };
  local $^W = 1;
  $_[0] == $_[1];
}
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-- iakobski

if( $num1 !~ /^\d+$/ )
   { warn "First value is not a number"; }
elsif ( $num2 !~ /^\d+$/ ) 
   { warn "Second value is not a number"; }
else
   { my $result = ( $num1 == $num2 ); }
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try a combination of eval and die for that. ex:

eval {
     if .... {
         die 'Error Message 1';
     else {
         die 'Error Message 2';
     }
};
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Just turn off warnings for that bit of code:

if(  do{local($^W)=0;  $x == $y  }  ) {
    # ...
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