Do you prescreen interested parties for a showing?

[George V.]

When a current apartment is rented with tenants, and you need to rent the place for when they leave, do you have them fill out an application first? I currently use Zillow for applying, but I'd have to tell prospective tenants to apply with credit check and a fee there. 

What is the best approach to prescreen tenants so that I don't waste my time and current tenants' time on someone who don't qualify?