In business, the following formula is used as an excuse: Sumimasen, Mōshiwakearimasen, Shitsureishimasu, Gomennasai. If you are late, for example, because of a transport problem that is not within your responsibility, apologize anyway. Whatever the reason, you have violated your promise... You must first apologize.
The first term that comes to mind to apologize in Japanese is す み ま せ ん Sumimasen.
You're probably already know this word, but think again, because it contains a lot more meanings than you might think ...