This is an old school trick, but if a cut is large enough to bother me, i put a bit of shoe goo in it, it keeps grit and stuff from working its way into the hole.

An other trick I use when i realize i have run over bits of glass; I run my gloved hand on the tire in an attempt to dislodge any bits that are stuck to the surface and may eventually work themselves through. Disclaimer: you may crash and die a terrible death while doing this.

Unfortunately this technique doesn't work well if you are running fenders.