English is slightly ambiguous here. The nature of the mapping between the (passive) subjects and the objects isn't inherent to this construction, there's just a strong tendency in how it is used.
We would generally understand
Only those who qualify will be awarded a certificate.
to mean that each person who qualifies gets an individual certificate. It's not impossible (but it would be very unusual) to use it to mean that all the qualifiers will get a single certificate to share between them. If you wanted to emphasize that there is a 1-1 mapping you would need to say something like
Only those who qualify will be awarded a certificate each.
or something similar. It does look odd in this particular instance, which suggests I've done it wrong :-)
I would also understand
Only those who qualify will be awarded certificates.
to probably mean that each qualifier gets one certificate, but it would also be common for it to mean that each qualifier gets several certificates. It could also mean that some qualifiers had to share one or more certificates between them, though again that would be very unusual. All that the plural "certificates" allows us to be certain of is that more than one certificate is involved overall.
Your other examples have qualifiers on them:
"Each student gets one pencil"
Using "each" here enforces the 1-1 mapping, where "students get one pencil" has only custom on its side, and "students get pencils" is ambiguous.
Having said all that, the "a certificate" version strongly implies the 1-1 mapping that you're after, but the "certificates" version weakly implies it too.