While marriage between same sex couples is still not legally recognized by the State of Hawaii, it is possible to register as a Reciprocal Beneficiary Relationship.  Here are the details from the Hawaii State Department of Health website:

"A reciprocal beneficiary relationship is a legal partnership between two people who are prohibited from marriage (HRS §572C-2). Certain rights and benefits which are presently available only to married couples are extended to the two individuals who enter into a reciprocal beneficiary relationship. Those persons entering into a reciprocal beneficiary relationship must register their relationship as reciprocal beneficiaries with the Department of Health."

Please follow this link for all the details on how to register for a reciprocal beneficiary relationship:

http://www.state.hi.us/health/vital-records/vital-records/reciprocal/index.html

If you have questions, please call the Department of Health, 808 586 4533.