Anyone with a computer can print a certificate, therefore they can mean nothing at all. Crooks on the internet play heavily on selling items with "certificates", these have no meaning or value and offer no guarantee of authenticity. Proper guarantees will describe an object in detail or include a photograph so that they can not be inter-changed with forgeries.
If a certificate is not backed by a professional association, you are relying 100% on the dealer being honest, it offers you no legal protection. Always ensure that you are supplied with a receipt: this must contain the dealer's registered trading address, registration number, date of sale, and value and nature of the goods.
A receipt offers some legal protection, especially in association with credit card payments.
What guarantees should I expect from a dealer?
A good dealer will unconditionally guarantee the age, description and condition of an object which they offer for sale. This goes far above the guarantees offered by most international auctioneers. This guarantee will not have a time-limit: if an item is mis-catalogued in any way, a reputable dealer will refund it at any point as long as they are still trading.
As well as the guarantee, a good dealer will also allow clients to return items bought from photographs (i.e. the internet) for a certain period after a sale if the customer feels they are not happy for any reason whatsoever: reputable dealers acknowledge that it is hard to evaluate works of art from two-dimensional images.
Some countries including the UK offer buyers statutory rights to return items bought in this way for two weeks after the sale, we extend this to one month to reflect realistic international shipping standards.