I'm simulating a large PCB (~2in x 0.5in) with many ports (44). It consists of a microstrip circuit and a large ground plane the size of the PCB. The circuit is the PCB for a band pass filter with a half octave bandwidth.

This thing take a long time to mesh and simulate.

So my question is, observing that increasing mesh densities only increase accuracy by ever smaller amounts, while increasing the computation time exponentially, what level of meshing density in cells/wavelength that will generally good results without going overboard on the computation time.

Also, if you compute the mesh at (for example) 4 GHz, can the S-parameter simulation be extended to higher frequencies (say 6GHz) without too much error?

This thing take a long time to mesh and simulate.

So my question is, observing that increasing mesh densities only increase accuracy by ever smaller amounts, while increasing the computation time exponentially, what level of meshing density in cells/wavelength that will generally good results without going overboard on the computation time.

Also, if you compute the mesh at (for example) 4 GHz, can the S-parameter simulation be extended to higher frequencies (say 6GHz) without too much error?

The best advise is to do a couple of tests with a typical circuit. Run one simulation with one coarse mesh setting, for instance 20 cells / wavelength. Then run another simulation with 30 cells / wavelength. Compare the results. If the results changed 3%, then you can assume that the results will change less than 3% if you increase the mesh with another 50%, e.g. from 30 cells to 45 cells per wavelength.

How many iterations you need to do depends on how much the results changed and what accuracy that you require for the simulation. You will however build up a feel for what's required once you've done this exercise a few times on a couple of typical circuits.

Some types of circuits seems to require a finer mesh than others. I've seen a few antenna designs which required a very fine mesh (>100 cells per wavelength). While other designs required only 20-30 cells per wavelength to produce good data.

Finally a comment about your question regarding the 4 GHz mesh frequency and simulating it up to 6 GHz. Assume you mesh the circuit with 30 cells per wavelength at 4 GHz. Then you simulate this circuit up to 6 GHz. At 6 GHz the mesh density is 30/(6/4)= 20 cells per wavelength. Does this give good data or not? You have to run a few tests, as described above, with different mesh densities on the circuit to get a feel for what it does to the accuracy.