The New York legislation provides an extensive description of the "religious exception:" 

"Notwithstanding any state, local or municipal law, rule, regulation, ordinance, or other provision of law to the contrary, a religious entity as defined under the education law or section two of the religious corporations law, or a corporation incorporated under the benevolent orders law or described in the benevolent orders law but formed under any other law of this state, or a not-for-profit corporation operated, supervised, or controlled by a religious corporation, or any employee thereof, being managed, directed, or supervised by or in conjunction with a religious corporation, benevolent order, or a not-for-profit corporation as described in this subdivision, shall not be required to provide services, accommodations, advantages, facilities, goods, or privileges for the solemnization or celebration of a marriage.

"Any such refusal to provide services, accommodations, advantages, facilities, goods, or privileges shall not create any civil claim or cause of action or result in any state or local government action to penalize, withhold benefits, or discriminate against such religious corporation, benevolent order, a not-for-profit corporation operated, supervised, or controlled by a religious corporation, or any employee thereof being managed, directed, or supervised by or in conjunction with a religious corporation, benevolent order, or a not-for-profit corporation.

"Notwithstanding any state, local or municipal law or rule, regulation, ordinance, or other provision of law to the contrary, nothing in this article shall limit or diminish the right ... of any religious or denominational institution or organization, or any organization operated for charitable or educational purposes, which is operated, supervised or controlled by or in conjunction with a religious organization, to limit employment or sales or rental of housing accommodations or admission to or give preference to persons of the same religion or denomination or from taking such action as is calculated by such organization to promote the religious principles for which it is established or maintained.

"Nothing in this section shall be deemed or construed to limit the protections and exemptions otherwise provided to religious organizations under section three of article one of the constitution of the state of New York.

... A refusal by a clergyman or minister as defined in section two of the religious corporations law, or Society for Ethical Culture leader to solemnize any marriage under this subdivision shall not create a civil claim or cause of action or result in any state or local government action to penalize, withhold benefits or discriminate against such clergyman or minister."

Click here for a link to this text. An accompanying memo describes the bill in total.

In Maryland, religious protections came up throughout the same-sex marriage debates in the Senate and the House of Delegates. Here's the language upon which the Senate settled:

"Notwithstanding any other provision of law, a religious organization, association, or society, or any nonprofit institution or organization operated, supervised, or controlled by a religious organization, association, or society, may not be required to provide services, accommodations, advantages, facilities, goods, or privileges to an individual if the request for the services, accommodations, advantages, facilities, goods, or privileges is related to: the solemnization of a marriage or celebration of a marriage that is in violation of the entity’s religious beliefs; or the promotion of marriage, through religious programs, counseling, educational courses, summer camps, and retreats, in violation of the entity’s religious beliefs.

"A refusal by an entity described in subsection (a) of this section to provide services, accommodations, advantages, facilities, goods, or privileges in accordance with subsection (a) of this section may not create a civil claim or cause of action or constitute the basis for the withholding of governmental benefits or services from the entity.

"AND BE IT FURTHER ENACTED, That: Notwithstanding any other provision of law, a fraternal benefit society described in 8–402 of the Insurance Article that is operated, supervised, or controlled by a religious organization may not be required to admit an individual as a member or to provide insurance benefits to an individual if to do so would violate the society’s religious beliefs. A refusal by a fraternal benefit society described in subsection (a) of this section to admit an individual as a member or to provide insurance benefits to an individual may not create a civil claim or cause of action or constitute the basis for the withholding of governmental benefits or services from the fraternal benefit society.

Here's the text of Maryland's civil marriage bill as it passed out of the Senate.