Their new status means they can qualify for lower car insurance premiums because they are no longer considered “single males.” And they hope their marriage will give them more legal standing if their son, Joshua, 5, lands in the emergency room because of his asthma. The last time he was admitted, the pediatric nurse told the two dads that she needed to speak with the child’s mother.

But, Mr. Friedman said, they are well aware that their marriage carries no weight when it comes to, say, filing their federal tax return (though they can file a joint state tax return, which will allow them to keep more of their earnings). And the marriage certificate is flimsy when the couple leaves New York, which honors same-sex marriages performed elsewhere. On family vacations, the pair will continue to bring along a slightly torn manila folder, stuffed with documentation  birth certificates, health care proxies, powers of attorney and all of their son’s adoption records  that proves they are a family.

“Our hope is that also providing a marriage license might help provide additional documentation for proof of how we are all related,” Mr. Friedman said. “I want to make sure my son is taken care of if something were to happen to me.”

The list below outlines the benefits same-sex married couples (and those with civil unions) generally receive, as well as what they still need to be concerned about. These issues are not as complicated for opposite-sex couples, because they receive many more rights when they marry, regardless of where they live, and those rights are broadly recognized.

MEDICAL POWER OF ATTORNEY Married or not, all committed same-sex couples should consider a power of attorney for health care or medical matters, which appoints a person to make medical decisions for you when you cannot do so. It is also known as a health care proxy, among other things, depending on where you live. The document should include an authorization under the Health Insurance Portability and Accountability Act to provide access to medical records. You may also include a hospital visitation directive to specify who can visit you in the hospital.

Another important document is a living will, which specifies which medical procedures may or may not be done. “It is an important document for anyone, but more so for same-sex couples because we could have family members come in and say, ‘No, I know better and this person has absolutely no standing,’ ” said James Tissot, a New York financial planner.

DURABLE POWER OF ATTORNEY If one partner becomes incapacitated, a durable power of attorney gives the other partner authority to handle financial and legal affairs, like paying bills.