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I'm just wondering, if one were to run a $\ce{^{11}B}$ NMR on a boron containing sample in a borosilicate tube, how could we separate the spectra of the tube and the sample?

Apart from using a different tube - Perhaps through a pulse sequence like BIRD for $\ce{^1H/^13C}$?

Or decoupling - which I've only just started to learn about and don't really understand?

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The borosilicate tube gives a very broad signal, the signals from the boron compounds you're measuring should be much sharper. If your samples are concentrated enough and have reasonably sharp lines, that should be sufficient to distinguish them from the broad background signal from the NMR tube.

You could of course also measure an identical NMR tube with the same amount of solvent, but without your boron sample. Comparing this with your real sample should make it easy to identify which signals are background from the tube.

And of course you could use an NMR tube made from a different material.

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You'd run the nmr in a quartz tube, or a tube made from some other non-boron containing material.

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    $\begingroup$ Most NMR probes have boron-containing inserts that separate the NMR tube from the coil surface, and these will also contribute to 11B background. If investing in quartz tubes, it is important to check the probe design, and select the right one for the job. $\endgroup$ – long Mar 10 '15 at 21:35

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