So, to summarize, it's simple but not easy: Start with "I'm sorry. That was my fault" (your feeling). Mean it! Then empathize with the other persons's feeling and situation. Do it authentically, don't extend it so it sounds manipulative. If he/she is ready to shift from emotion/threat response to content/facts, briefly explain what happened. It's important to understand if you've been just sloppy with your time management or anything else was more important, OR you had an important client meeting that unexpectedly lasted longer than planned. Later, show what you've learned and what you will do differently next time. And learn!