Museum-hopping on holiday gets expensive fast. Admission fees of $20-30 per institution add up over a long weekend, and that is before gift shops and special exhibits. But there is an under-the-radar workaround: a reciprocal membership network that can unlock free or discounted entry to roughly 1,500 museums across North America — all through a single sign-up.

The scheme is NARM, the North American Reciprocal Museum Association. You cannot join directly; instead, you buy a membership at any participating museum that includes NARM privileges. A travel writer testing this across Connecticut joined the New Britain Museum of American Art at its $125 'Circle Membership' level, which comes with NARM access. That single purchase covered unlimited return visits to the home museum (normally $22 a pop) and paid for itself after visits to just five other institutions. In pricier cities the maths works even faster — New York's Frick Collection, a NARM participant, normally charges $30 per adult.

There is no cap on how many member museums you can visit in a year, or how often you can return to the same one. Members also get discounts at museum shops and on ticketed events. The network spans the United States including Puerto Rico, plus Canada, Bermuda and the Cayman Islands.

If science and kids' attractions are more your thing, two alternatives are worth knowing. The Association of Science and Technology Centers runs a Passport Program with over 700 venues — think the U.S. Space & Rocket Center in Huntsville, San Francisco's Exploratorium, Philadelphia's Franklin Institute and Houston's Perot Museum — and reaches institutions in countries from Australia to Singapore and South Korea. The Association of Children's Museums offers a reciprocal network giving 50% off at around 200 kids' museums nationwide.

Read the fine print before signing up. ASTC memberships generally exclude institutions within 90 miles of where you live, so locals can visit their home museum freely but not its neighbours. NARM has a similar, smaller catch: some museums enforce a 15-mile exclusion radius. And reciprocity is not always total — a few venues offer discounts rather than free entry.

Even without paying for a membership, free museum access may already be sitting in your wallet. Bank of America cardholders get free admission on the first full weekend of every month at participating museums, including the Metropolitan Museum of Art in New York and the Georgia O'Keeffe Museum in Santa Fe. Library cards open doors too — California's Discover and Go, New York City's Culture Pass and family passes from Massachusetts Libraries all offer free or discounted local admissions. EBT cardholders qualify through Museums for All, and military families get free entry to some 2,000 museums, zoos and nature centres under the Blue Star Museums program between Armed Forces Day in May and Labor Day.

For anyone planning a culture-heavy city break, a single membership could slash admission costs before you even leave home.