ROCKPORT, Texas—After Hurricane Harvey thrashed their coastal home here last year, tearing off chunks of roof and leaving a sodden shell, Bill and Susan O’Bryant vowed: Never again.

They are now rebuilding a well-armored home, adhering to stringent building standards devised by the insurance industry that exceed local code requirements. The house’s roof, floors and foundation are fastened together with steel straps, the windows are made of impact-resistant glass, and the roof is specially sealed and nailed down.

“We really wouldn’t do this any other way,” said Mr. O’Bryant, a 74-year-old retired restaurateur.

As the start of a new hurricane season looms on June 1, homeowners along this stretch of Texas coast—which Harvey pounded with 130-mile-an-hour winds before steering north to drench Houston—are grappling with how to build back stronger. Some officials and residents are calling for stiffer standards to create sturdier homes, while others fear that excessive requirements could financially burden homeowners.

It is a debate that has surfaced repeatedly in coastal communities from Texas to New York in the wake of ruinous storms. In an era of rising sea levels and intense hurricanes, measures to harden buildings are key to ensure communities remain viable, risk consultants say. They also make properties more attractive to insurance carriers—essential to create a robust insurance market that can provide homeowners with sufficient coverage at affordable rates.