A website like www.askmid.com will tell you if you car is on the database or not. However, be warned as these things aren't perfect. Once you have found out if you car is insured or not.
Unfortunately, I cannot find a website or a way of finding out if a car is insured with a particular insurer easily. The only way I can think of suggesting is to ring around the companies you think you might have used. However, to aid you I would suggest this. Enter your details on a price comparison website. This is because you are likely to have gone with the cheapest insurance you can find (as any sensible person would). Therefore you might want to work you way down that list. If this fails then it would be worth reinsuring your car, and putting the paperwork in a place you know you will not lose it.