Our house insurance has a clause where there is a replacement amount per item or a total contents replacement cost, whichever is lower. The replacement per item amount is a maximum of $1000, that would cover most items in my collection. I do have a couple of non-transformer antiques in the house which are worth more and are separately insured. To do that I had to prove what they are worth. Insurance companies can walk you through what they need to prove value but usually its just objective evidence that something is worth a certain amount (this can be a licensed appraiser, they do exist) or proof that similar items have sold for similar amounts in the recent past. In the case of my collection its simply not necessary.
The other question is how important to you is your collection? Before you instinctively answer "very", assume your house burnt down. At what point would you get around to replacing everything in your collection? In my case I'd replace the appliances, my children's things, the electronics, beds and furniture and then get around to my collection. At that point I'd probably still have some of the lump payment left to replace some of it anyway.
Just my two cents worth. If you learn anything that conclusively proves me wrong let us know, I'm working on 10 year old information here.
Oh and if anyone is interested in pursuing the appraisal route, I'd be curious as to your experiences. I deal with appraisers a bit at work (for taxes not insurance). A good resource is as follows.
http://www.isa-appraisers.ca/
