My father received a certificate from the embassy in 2003 titled "Confirmation of the acquisition of Dutch citizenship by option," stating that he has Dutch citizenship. However, he never applied for a Dutch passport; he died in 2007. I am now 19 years old and my sister is 13. Will either of us be able to obtain Dutch citizenship? Does he have to be alive to declare this for us?
It may depend on why your father was able to use the option procedure to acquire Dutch citizenship; at least some option procedures are retroactive. More importantly, it depends on whether your father was Dutch when you and your sister were born.
For example, if your father was Dutch from birth, but lost that nationality because he was born abroad and lived abroad for more than 10 years after his 18th birthday, then his option procedure will have restored his Dutch citizenship retroactively ("met terugwerkende kracht"). In this case, it does not matter when you and your sister were born.
If your father's option procedure is not retroactive, then you and your sister can be Dutch only if you were born when he was Dutch.
In addition, he must have been married to your mother or else he must have acknowledged you formally as his children.
If these conditions were met, then you are already Dutch and all you need to do is apply for a passport.
The only declaration that might be needed would be the "acknowledgement" that you are his children, which isn't necessary if he was married to your mother at the time of your birth.
It depends, it depends on where you live and have lived. You also may have to renounce your existing citizenship.
Whether or not you are eligible for the "option" to become dutch depends on these criteria: https://ind.nl/en/dutch-citizenship/pages/option.aspx
As an adult it sounds like it's unlikely for you and perhaps possible for your sister as a minor. I would reach out to your local dutch embassy or consulate for more information.