Looking on the internet deeply has found these results:

my apologies is the most popular phrase on the web.

i do apologize 1513,000 results on the web	my apologies 1779,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
I do apologize for these consent forms. And I do apologize for that. I do apologize for any inconvenience. I do apologize, little lady, but it's better for you if you don't see where we're going. I do apologize, ma'am, but the guests directly overhead, a rather large gentleman, broke his toilet. I'm so sorry to have kept you waiting, your Lordship. I do apologize, please forgive me. Once again, I do apologize for breaking said trust. I do apologize for this necessary precaution, Miss...	Dec 18, 2008 ... I tend to use "my apologies" when I'm being more formal or writing to someone, for example "Please accept my apologies for...." Where May 18, 2015 ... When you write a letter, and mention the phrase my apologies. How is ... "My apologies" is effectively a more formal/posh way of saying "sorry". Please give my apologies [=excuses] to your cousin. I'm sorry that I won't be able to come to the wedding. I made my apologies and left. [+] more examples ... as if I do ... Aug 22, 2015 ... "My apologies" only addresses the issue of apology, that somehow an apology ought to be offered, so here is one, regardless of whether there ...

i do apologize

1513,000 results on the web

my apologies

1779,000 results on the web

More popular!

I do apologize for these consent forms.
And I do apologize for that.
I do apologize for any inconvenience.
I do apologize, little lady, but it's better for you if you don't see where we're going.
I do apologize, ma'am, but the guests directly overhead, a rather large gentleman, broke his toilet.
I'm so sorry to have kept you waiting, your Lordship. I do apologize, please forgive me.
Once again, I do apologize for breaking said trust.
I do apologize for this necessary precaution, Miss...

Dec 18, 2008 ... I tend to use "my apologies" when I'm being more formal or writing to someone, for example "Please accept my apologies for...." Where
May 18, 2015 ... When you write a letter, and mention the phrase my apologies. How is ... "My apologies" is effectively a more formal/posh way of saying "sorry".
Please give my apologies [=excuses] to your cousin. I'm sorry that I won't be able to come to the wedding. I made my apologies and left. [+] more examples ...
as if I do ...
Aug 22, 2015 ... "My apologies" only addresses the issue of apology, that somehow an apology ought to be offered, so here is one, regardless of whether there ...