Start with the yacht, not the company. In Malta, the licence that matters is the Transport Malta commercial registration held by the specific vessel for carrying paying passengers. Ask for the yacht's name and its licence number in the same sentence. A company with an impeccable website and a yacht that is only privately registered cannot legally take your money for a charter, and its insurance will not respond if something happens to a guest.
Then the insurance. You want passenger liability cover naming that yacht, and you want the certificate number. Hull and machinery insurance protects the owner's asset, not your family. Any operator who charters regularly has this document to hand and will send it without hesitation; hesitation is the answer.
Then the crew. Ask the skipper's name, their licence and how long they have worked Maltese waters. A company that cannot tell you who is driving your yacht three weeks out is either overbooked or planning to sub-contract the day to whoever is free, which is exactly how a charter ends up on the wrong route in the wrong wind.
Finally the contract. A legitimate quote states the yacht, the licensed guest capacity, the crew, what the price includes, the extras and their prices, the cancellation terms, the bad-weather policy and the VAT treatment. Weekly and superyacht charters should be on a MYBA-style agreement. If nobody will put it in writing before payment, the writing is not the problem — the operator is.