What do you do if you are unable to find a marriage document on Ancestry Library Edition or Family Search?
Try obtaining the marriage license from the county clerk's website. (For Cook County, this would be Cook County Genealogy.) Do not stop with using the index; you may have to purchase a digitized copy of the original document. The cost is small compared to its genealogical value, because there will be a date and an address for where the marriage took place.
Research this address. It may turn out to be for an organization such as a church which is not included in microfilmed holdings in the catalog of the Family History Center.
Contact the organization and ask how to obtain a copy of a record for a marriage that took place there.
The procedure may vary. But usually they will provide the necessary documents in exchange for a small fee.
This copy may turn out to be a gold mine of information including names of parents of bride and groom, location of birth and / or baptism of bride and groom, names of witnesses, etc. Sometimes names will be written in an unfamiliar spelling, which may turn out to be significant for your research.
Try this approach if you are stuck, it may provide you with many new leads.