Supercontinuum generation using chip-integrated photonic waveguides is a powerful approach for spectrally broadening pulsed laser sources with very low pulse energies and compact form factors. When pumped with a mode-locked laser frequency comb, these waveguides can coherently expand the comb spectrum to more than an octave in bandwidth to enable self-referenced stabilization. However, for applications in frequency metrology and precision spectroscopy, it is desirable to not only support self-referencing, but also to generate low-noise combs with customizable broadband spectra. In this work, we demonstrate dispersion-engineered waveguides based on silicon nitride that are designed to meet these goals and enable precision optical metrology experiments across large wavelength spans. We perform a clock comparison measurement and report a clock-limited relative frequency instability of at seconds between a 1550 nm cavity-stabilized reference laser and NIST's calcium atomic clock laser at 657 nm using a two-octave waveguide-supercontinuum comb.