Metacam, a non-steroidal anti-inflammatory is quite safe. There have been toxicity studies performed with overdoses far greater than a double dose.
So, I am not worried about the organs. However, is there a chance for gastrointestinal upset? Yes
So, you will need to keep an eye out for any vomiting, diarrhea, loss of appetite, or blood in the stool for the next 24 to 48 hours.
Otherwise, there is no indication to induce vomiting, and I would resume your normal dose or directions from your vet for tomorrow.
If illness was to develop, a vet visit for some basic supportive care should be all that is needed.
Also, to help the stomach a bit, you could give some Pepcid A.C. antacid.
Yes, the same Pepcid people take. You could give a 1/2 tablet of a 10mg regular strength Pepcid.