Definitely do your research on sites like Autorader or Parkers or What Car, as the first offer they make will almost certainly be laughable (in my experience) and you will need to be sure of your position when you reject it. You are under no obligation to accept an offer you are not happy with.
In the past I had to hold out for the 3rd offer from an insurer before getting one which reflected the MARKET value of my car. Be sure that you don't over estimate from a sentimental point of view, but have some comparison evidence to reply with.