The auto insurance coverage purchased that is associated with the SR-22 form will be rated according to all the factors that normally go into rating a policy, regardless of the SR-22 form filing. The rates are not different if you are getting an SR-22 or not.
As for the actual SR-22 form, insurance companies are typically allowed to charge a nominal fee for filing the financial responsibility form (certificate) to the state. State laws differ however the SR-22 form filing fee is typically only $15 to $25.
Your driving record is a rating factor in the cost of auto insurance so the reason that you are required to acquire and maintain the SR-22, such as reinstating your license after a DUI suspension, may affect your car insurance premiums however the SR-22 form itself does not beyond the filing fee.
To obtain a quote and find out how much an insurance policy that includes a SR-22 filing will cost for you, click here.