Ditto on @dlochner post.The take home is when going under a bridge that is close to the boat's air draft, don't go at high tide, especially in a place where there is a significant tide. Cape May is around 4 feet.
In addition, be particularly careful where the variation in High Tide is significant. It effects the MHW listed where some High Tides are well above the MHW. For instance, here in Beaufort SC the McTeer Bridge is a "nominal" fixed 65 foot bridge. Mean High Water is 7.6 feet (see below), which is the basis for the bridge design clearance. However, we have high tides that routinely range between 9 feet and 6 feet. So on one of those days with high tides above 7.6 feet you have to be very mindful of not only your air draft but the datum, the current tide level and its relationship to MHW etc. Note, the highest tide observed was over 11 feet. In places effects of prolonged wind can drive water up and the clearance can be even less!
Like @dlochner said, know your "loaded air draft" and be mindful of the variables that effect the clearance that is actually available.
Datums - NOAA Tides & Currents