Measurements did not match the expectation, so I documented the process.

1. A single-layer patch is inherently narrowband, typically 2-5 percent for VSWR 2:1.
2. Stacked parasitic patches or an aperture-coupled feed with a thick low-permittivity substrate broaden it.
3. Lower substrate permittivity buys bandwidth but increases size, and surface waves become an issue above roughly 0.3 of the substrate thickness.
4. If you need more than about 10 percent bandwidth, consider a different topology rather than fighting the patch.

Would like to hear real-world cases.