I'm not sure there is a "best" insurance company for these vehicles.
Ideally it means that you have an agreement with a company for an agreed upon value should something happen to the vehicle.
If you don't have an "agreed upon value" in advance, you might make payments thinking the vehicle was fully covered, but then find out in the case of a loss that the insurance company figured your car was fully depreciated in value (as an automobile) and would "total" the car at some ridiculously low amount.
Different companies may also have different limitations or restrictions on use.
Although I personally use Hagerty, I've never had a claim so I can't say they are the "best".
That being said, I have not heard any horror stories. Actually I have heard some, but they usually involve people who did not have their cars insured. I heard one story from a person that under-insured their car and it fell off the back of a flat bed tow truck while it was being moved. It totaled the car. Their own insurance did not fully cover the loss. They figured the tow company insurance would pay, but of course the tow company insurance decided the car was worth very little and said "sue us". Sounds fun.
It would be interesting to see how the different companies treat your Frisky.
If it is in their database there is not usually a problem, but I know someone who had a very rare oddball car, the only one of its kind in the USA and Hagerty gave them a real hard time when they initially tried to insure it until they provided a lot of documentation of the car's condition and proven value before deciding on an agreed upon value ($12K at the time about a decade ago).
Might seem silly now, but insurance fraud happens and people will do all sorts of wacky things like buy some wreck of a rare car, insure it for a very high agreed upon value and then claim it was stolen, trying to collect restored value on a junker after only a few payments.
While shopping around for insurance coverage, make sure you compare what the policies say as far as limitations of use and terms of storing the vehicle. If you claim the vehicle is stored in a garage but actually store it outside on the street while cleaning out your garage and it gets damaged, will the insurance company pay? I only say this because
A: the car was not stored in the place agreed upon
B: the car was not going to or from a car show or something
I think you should look up some companies for quotes, but also do a search for their name with the word: COMPLAINT and see if anything of value comes up to help.
In addition to Hagerty
www.hagerty.comthere is Grundy:
www.grundy.comJC Taylor:
www.jctaylor.comand others.
I have heard from other vintage microcar owners that places like State Farm and Progressive are getting into the collectible car insurance game, so it doesn't hurt to contact your regular insurance company and see what they say as well. But again- it's how you are treated when you have a claim that really matters.
Post back what you find out after shopping around.