How to apologize (in personal and professional life)?

The way I'd apologize would depend on a few factors:

• How visible was the mistake? Did it impact 1 person or 10 people?
• What was the impact of the mistake? SEV0 or just a minor annoyance (like being a few min late to a meeting)

Also, in the corporate world, I'd focus less on the apology and more on the impact of the business. (I agree with what you mentioned: the harm is not felt at an individual level for professional relationships.) A general format to use:

• Take responsibility for what happened
• Share the context of why the incident happened
• Talk about the impact to the business
• Talk about steps you're taking to prevent this from happening in the future

As I write that, it sounds like a SEV review, which is not a bad analogy honestly 😅

In your work life, there’s so many different contexts that I don’t really know that there’s blanket advice.

I would measure how much contrition is necessary based on how impactful the mistake was. Did the meeting proceed and the outcome was reached without you, but you now require someone to debrief you? Can you get context from notes or a recording? If a group of people all dedicated time, and your absence meant the meeting had to be rescheduled, that is a huge trust buster and you owe them time, IMO.

From there, what is the content of the apology? Generally any apology must:

1. Take sole responsibility for your actions and the outcome.
2. Describe how you intend to make it right, validate that this is appropriate, and pivot if it isn’t.
3. Describe what you will do to prevent reoccurrence. Not “it won’t happen again”, but “change notifications for meetings and add them to mobile devices with notifications” or “write down comments and re-read them thoughtfully before sharing”. Whatever it is, it’s your responsibility and needs no assistance from others.
4. Not blame others, expressly or implicitly
5. Not contain “but”, “however”, or express that the reason for the apology is because you were told to, are required to, or is based only on their feelings. I.e. “I’m sorry you were mad”
6. Acknowledge that trust was damaged, and you are responsible for repairing it. Recognize this won’t be immediate, and you accept that extra verification or follow-up will be required in the future.

From there… you’re sort of at their mercy. Don’t grovel, but be sincere.

For missing a meeting, it's fine to say "I am so sorry I missed the meeting. I completely lost track of time." If you can add comments on the meeting doc for larger group meetings or take the initiative to reschedule a smaller, 1:1 meeting, that will signal that you are truly invested in the topic.

The important thing is that you learn from the mistake after apologizing. If you keep making the same mistake over and over, all previous apologies will start to sound disingenuous. It will sound like you are making excuses, and you won't sound trustworthy. Can you come up with an action item for yourself to prevent yourself from missing another meeting? That might look like setting an alarm on your phone 10 minutes before a meeting.