You can accomplish this by using the s/// replace function:

my $text = "I saw the panda myself,\nbut Amy did not.\nA var a.my";
my $regexp = qr/(a[ .]*my)/i;

$text =~ s/$regexp/'~'.uc $1.'~'/ge;
print "$text\n";
[download]

gives

I saw the pand~A MY~self,
but ~AMY~ did not.
A var ~A.MY~
[download]

Here, I have tested for optional spaces and periods. Generalization to other punctuation is straightforward.