Why upsample before modulation? We're doing a project in which we're sending an OFDM frame, modulated to some appropriate carrier, over a channel. Before modulating, we are instructed to upsample and low-pass it. Is there a good explanation this should be done? We have full control over sample rates at both Tx and Rx. 

I guess it has something to do with an interpolated signal resembling a smooth signal more, which makes it somehow more appropriate for multiplying by a modulating function. But this is very imprecise and hand-wavy.

Can anyone explain why one would want to upsample, given that there are no differences in sample rate between transmitter/receiver?
The reason is aliasing. Because the modulation is digital, on the discrete signal, the sampling frequency should be high enough that the channel's frequency band does not extend beyond the Nyquist frequency = sampling frequency / 2. If the sampling frequency is too low, the frequencies beyond the Nyquist frequency will alias to other frequencies, meaning that you would be transmitting at the wrong frequency. By lowpass filtering before modulation, you are removing spectral images of the baseband. If those are not removed the signal has frequencies outside the baseband and similarly the modulated signal won't be contained in the channel's band.