Consider the situation for which you want to apologise to my boss. Even though you are in his submission, this does not mean that fault automatically falls on you. In that case, when he as leader could not adequately provide for the completion of your work order, did not create the conditions for its fulfillment in time, should not be held responsibility. To under such circumstances is not to apologize and not to apologize all the problems beyond your control, but requires management intervention, setting forth the memo. In this situation, you will be calm – your innocence is proved.
To apologize to the head in that case, when you really failed him and did not do in time what you instructed. Because you are an adult and should understand that in the workplace you are charged with unconditional performance of their duties. If you come into the office to apologize for something that didn't show up for work on time, resulting in an important contract was not signed, but let that slept or ran to the Barber, it is clear that the forgiveness you are unlikely to get.
Going to the head with the apology, you must be sure that the reason you called, is really respectful. Best of all, if it is from the category of farce majeure, to provide or inform you about which was really impossible. And keep in mind that it must be really so - to lie to you, it will be difficult, and head your probably not stupid, to catch you in a lie for it will not be difficult.
In order to get forgiveness, not only to refer to the cause. By and large, a personal apology and repentance useless. Come to the head office with a ready alternative solution to the problem, the perpetrator of which you have become. Rest assured that even if this option is not able to fully compensate for the losses the company suffered because of you, the forgiveness you deservedly receive.
Remember the tone that usually apologize. It should not be defiant or condescending. Try to keep your voice clearly sounded notes of contrition and regret. Be natural, and your apology will be accepted graciously.