Use double MAC technique for checking MACs
Comparing a received MAC to the expected MAC in constant time is tricky in high-level languages because the compiler, runtime and JIT may optimise the comparison code so that it no longer runs in constant time. The adversary may be able to use the timing of the comparison to discover how many bytes of the received MAC match the expected MAC.
To avoid revealing this information, the recipient can calculate another MAC over each MAC and compare the outer MACs. The adversary can use the timing of the comparison to learn the position at which the outer MACs differ, but that doesn't reveal the position at which the inner MACs differ.
The MAC is being used as a PRF. It seems like this technique could also be used for validating signatures -- the validator can use any MAC key (not necessarily shared with the signer) to calculate MACs over the received and expected signatures, then compare the MACs.