You're late to the meeting, the party, and the appointment, the anything. Natural instinct is to slink in with a mortified expression, and immediately blurt out an excuse . . . before even sitting down! "The traffic was terrible." "My dentist's appointment ran late." "I had to take my pet to the vet," or "my kid to the doctor" ad nauseam.
Don't demean yourself like that! Don't slink in like a panting dog brandishing an excuse between his teeth. A gracious "Excuse me" suffices. Don't worry that the crowd is smirking, "Well what's his/her excuse?" Simply proceed proudly as though you are early.
Then LATER in the proceedings, find an unflustered way to honestly allude to the terrible traffic, the delayed dentist, the afflicted animal, or the sick little shaver. You come across as far more sincere, secure, and not obsessed with their opinion of you. (This definitely makes it go up a notch or two!)