Should I save for car repairs or pay off car loans early?

I’ve been thinking about our emergency fund. By next Friday, we’ll have a little over $1600 set aside. Yipee! Dave Ramsey says that the EF is separate from the 3-6 months of living expenses, and should be used just for emergencies. So now I am trying to predict what unexpected expenses may crop up in the next year or two. For us, the most likely culprit would be expensive car repairs.

(our house is in good shape – the roof and heating/cooling systems are still under warranty) Of course, there could be an awful family-type emergency too, but I’m thinking more of a predictable emergency here. So here’s my thought – I am considering calling our mechanic to find out about how much the worst-case scenario major repairs would cost.

I figure I can do this for each car (95 Volvo 940 wagon and 92 Honda Accord), and then try to get enough in the emergency fund to cover the single most expensive repair (ie new Volvo transmission or engine) My DH thinks I’m going a little overboard, and that we should worry about paying off the cars instead of saving for repairs that may not be needed. The Honda has only 85,000 miles, and the Volvo 115,000. Both are very reliable.

What do you think? Should I get aggressive about paying off the cars, or should I save enough to pay for a major repair the cars may not need any time soon? (We owe a little over 10K for both cars, and the Volvo will be paid off next summer)