The General Society of Mayflower Descendants has a service to compare a proposed lineage from a passenger on the Mayflower against previous research. The service was recently renamed Mayflower Lineage Match, announced in this blog post. Simply enter the proposed lineage on the Mayflower Lineage Match Form and submit online (or via paper). The current fee is $45, recently increased from about $25 due to the increased popularity of the service.
This previous research includes the Silver and Pink books of fifth generation descendants of Mayflower families. These books are described on their website here and are available for searching at AmericanAncestors.org through the database “Mayflower Families Fifth Generation Descendants, 1700-1880,” searchable (with a subscription) here.
The previous research also includes the previous application forms of members, over 90,000 files. This information is in the process of being digitized through partnerships with American Ancestors and FamilySearch. Even when this information is online, it will be only updated every five years, so the match service will be the most up-to-date method to check a lineage.
The lineage check is estimated to take three to six weeks. The submitter will then see if the lineage is viable or not, and if viable how many generations have been already verified. Membership then can be pursued by the Mayflower Member Societies in each state.
Some state Mayflower societies will perform a similar preliminary review for free, so check into that first.