I present a new approach at deriving far-infrared photometric redshifts for galaxies based on their reprocessed emission from dust at rest-frame far-infrared through millimeter wavelengths. Far-infrared photometric redshifts (FIR-$z$) have been used over the past decade to derive redshift constraints for highly obscured galaxies that lack photometry at other wavelengths like the optical/near-infrared. Most literature FIR-z fits are performed through $chi^2$minimization to a single galaxys far-infrared template spectral energy distribution (SED). The use of a single galaxy template, or modest set of templates, can lead to an artificially low uncertainty estimate on FIR-$z$s because real galaxies display a wide range in intrinsic dust SEDs. I use the observed distribution of galaxy SEDs (for well-constrained samples across $0<z<5$) to motivate a new far-infrared through millimeter photometric redshift technique called MMpz. The MMpz algorithm asserts that galaxies are most likely drawn from the empirically observed relationship between rest-frame peak wavelength, $lambda_{rm peak}$, and total IR luminosity, L$_{rm IR}$; the derived photometric redshift accounts for the measurement uncertainties and intrinsic variation in SEDs at the inferred L$_{rm IR}$, as well as heating from the CMB at $z>5$. The MMpz algorithm has a precision of $sigma_{Delta z/(1+z)}approx0.3-0.4$, similar to single-template fits, while providing a more accurate estimate of the FIR-$z$ uncertainty with reduced chi-squared of order $mathcal{O}(chi^2_{ u})=1$, compared to alternative far-infrared photometric redshift techniques (with $mathcal{O}(chi^2_{ u})approx10-10^{3}$).
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