When it's crunch time and a task requires I depend on an outside organization, I find it beneficial to double-book. Meaning I'll ask two, separate companies (or people) to commit to the same project, and see which comes through first.
This can be risky, especially when both pull through and you now have to tell one of them their services are no longer needed. It could be seen as poor business practice, and may even burn some bridges, but from my experience it's rare that both follow through. One will rise to the occasion, and the other will make an excuse.
Depending on the situation this may be cost-prohibitive, but when you can do it, you'll discover the company or person you can trust long-term. Someone you can faithfully depend on to get the job done, and many times that's work the risk.