If you look at the emission charts for such LEDs, they are not especially narrow band when compared to normal wavelength calibration sources. Something like the normal Mercury Argon reference source is commonly used for visible band spectrometer calibration, but the spectral lines stretch down to 922nm and have a MUCH lower FWHM. Then, while fewer in number, it's relatively inexpensive to get a hold of low power laser sources in the SWIR band on the used market - I picked up a 1550nm optical fiber verification source for ~$40 recently, and while it's only one wavelength and the choices are fewer, again the FWHM of the peak is much lower, so it would be much cleaner as a spectral reference.
That said, for just a visual indicator of SWIR performance for cameras or something, these sorts of sources may be the only real option. Of course to cover the band of available wavelength options you'd probably be dropping $100 or more before your driver circuit, but you could get a visual indicator of how far into the SWIR band your tester could see fairly easily.
For me, these LEDs are a tough sell for illumination outside of buying the specific wavelength you need to do your QA fault indication or similar using an SWIR camera, trying to make the equivalent of a LED light with variable color temperature but for SWIR would be an expensive proposition even though it could be fascinating for demonstration purposes or for configurable illumination.
Filtering is a possibility for similar performance when put in front of a broadband source, but it is difficult to find inexpensive bandpass filters well below visible light, so even if there are some good choices for communications applications, it may be tough to get together good choices to filter a broadband source.
For general illumination, my choice (and the cheapest choice) is a low color temperature halogen bulb and a filter. I picked up a 2900k bulb that accepts mains input and fits in a standard socket (though these should be available down to about 2700k), then you can put a hot mirror with extended range (many only go down to 1200nm or so), a cold mirror, or a long pass filter like RG1000 in front of it and so long as your housing can manage the heat, you have a VERY inexpensive broadband source.