Perhaps foremost, will the crematory allow you to tour its cremation facility. For obvious reasons you may not be allowed to tour the facility while a cremation is in progress, but any reputable crematory should make reasonable access available to you to tour the facility to observe how it is organized and maintained.
A fair question to ask is about training. Are the operators trained and is the crematory licensed? Is the license posted?
What is the age of the cremation chamber itself? Is it relatively modern equipment meeting emission, cleanliness and safety standards?
If your religious or philosophical values means you want to be present for the cremation process, it is fair to ask the cremation facility if and how they will accommodate the ritual that is right for you.
If you tour the crematory when no cremation is in process, it is fair to ask to view the inside of the cremation chamber. Is it clean and are the bricks, ceramics or other heat resistant material in good condition?
The cremation facility should provide, at a minimum, a comfortable environment for making arrangements and viewing a cremation in accord with its rules and regulations. Does the facility offer a chapel for a memorial service or perhaps an area for a food and beverage reception following a memorial service. Walk the facility and ask to visit these areas to assess how the look and feel to you. Is the facility convenient for you? Is parking available? Are the arrangement offices situated in a comforting landscape setting or a commercial store front – and does that make a difference to how you feel.
It is fair to ask the crematory for a schedule of their services and to determine when the cremated remains of the person you love or are caring for will be ready to be presented to you.