So do you mean that you DID indeed buy a replacement ticket (mode of transport being irrelevant) but that your insurance is not satisfied with proof of purchase of this new ticket taken together with proof of weather delay/late arrival?

Your OP makes no reference to new tickets; it seems as if the mere act of "no showing" is what you want to be compensated for:

"I missed the flight. I believe this falls under the travel insurance coverage that many credit cards provide."