How do you apologize to someone who seems like they are still mad?

Send a message.Saying that you want to apologize properly but you understand they may not feel ready to hear from you you,yet Ask them is it ok for you to call or would they prefer you try later.

Sending the message doesn’t put them on the spot and let’s them know you realize you messed up, which may help calm them. If you don’t hear from them in 24 hours, give them a call anyway.

Hmmm....they could be 'still mad' simply because you haven't tried to apologize yet? At any rate, it's never a bad time to say you're sorry. :)

Be sincere. Don't make excuses. Say that you understand that they are angry and you are sorry you reacted the way you did.

Because they are still mad doesn't mean to say you can't apologise [i]if[/i] you think you said something out of order. It could be said the sooner you try to make amends the better you might appear to them; whilst it should be said that, sometimes, an apology might be hard for some to accept until things cool down. But in any event, you making the first, and quickest, attempt to put things to rights can never be said to be a bad thing.

Give them some more time then apologize and explain the reason for your extra sensitivity if you haven’t already.

You've gotten lots of good advice. I would just add that after the apology, you ask them to please forgive you.