"I was not late, I was just fashionably delayed"
Step 1: Claim you had a family emergency. This is always a good option, as who doesn't love a good family emergency?
Step 2: Claim you were held up by a medical emergency. But only if you're willing to share graphic details, of course.
Step 3: Claim you were stuck in traffic. Just make sure you're not actually stuck in the meeting's parking lot.