Debbie, I'll tell you what worked for us.

When Chester was a pup, we started a savings account and took the monthly premiums and put it in that account each month. This worked best for us, we kept our money, but still had "insurance" that we could afford any medical situations that came up. This has proved to be invaluable. We also deposited any extra cash that we could come up with from each pay period. Over time we were also able to increase the money amount that we deposited, as we paid off other bills, got raises, etc.

Now we have a nice savings account that we've used several times for Chester (the girls are healthy as horses). We've had bladder stone surgery, allergy testing done 3 times, and several middle of the night emergency vet visits. We had no worries about paying for these emergency situations. Now, this wouldn't have helped us much in the beginning of Chester's life, as there wasn't much money in the account. But over the next four years or so until we had to use it, we had built up quite a bit of an emergency fund. His bladder surgery was well over $1000, and the overnight stays have been $400+ each time.