The band-limited coronagraph is a nearly ideal concept that theoretically enables perfect cancellation of all the light of an on-axis source. Over the past years, several prototypes have been developed and tested in the laboratory, and more emphasis is now on developing optimal technologies that can efficiently deliver the expected high-contrast levels of such a concept. Following the development of an early near-IR demonstrator, we present and discuss the results of a second-generation prototype using halftone-dot technology. We report improvement in the accuracy of the control of the local transmission of the manufactured prototype, which was measured to be less than 1%. This advanced H-band band-limited device demonstrated excellent contrast levels in the laboratory, down to 10-6 at farther angular separations than 3 lambda/D over 24% spectral bandwidth. These performances outperform the ones of our former prototype by more than an order of magnitude and confirm the maturity of the manufacturing process. Current and next generation high-contrast instruments can directly benefit from such capabilities. In this context, we experimentally examine the ability of the band-limited coronagraph to withstand various complex telescope apertures.