Final answer:
Two alternate methods of certifying eligibles are the top-two primary method and obtaining sufficient signatures from registered voters to bypass the party nomination process.
Step-by-step explanation:
The question refers to the certifying eligibles methods used within the political election process, particularly for nominating candidates for office. Two alternate methods used for certifying eligibles after the primary elections are the top-two primary method and the use of obtaining a significant number of signatures from registered voters. The top-two primary, sometimes called a jungle primary, involves all candidates running against each other regardless of party affiliation, with the two candidates receiving the most votes becoming the final candidates for the general election. On the other hand, a candidate can also be placed on the ballot by receiving enough signatures from registered voters, bypassing the traditional party nomination process.