For 2023, you can save up to the maximum contribution limit of $3,850 for an individual HSA health plan and $7,750 for a family HSA health plan each year.
If you are married and your spouse has a family HDHP, then both spouses are determined to have family coverage. This is true even if one spouse has a family plan and the other has a self-only plan. Each spouse may have an HSA, and together you may contribute up to the family limit. You may not each contribute up to the family limit.
If you are age 55 and older you may contribute an additional $1,000 to your HSA. This is a “catch up” contribution that may be made each year that you are eligible for a HDHP. You may no longer contribute once you enroll in Medicare.