I know patch antenna dimensions can be calculated easily but how big(width and length) of a substrate have to be?And what about its exciting ports(in case of waveport and lumped port)?
In practice, to avoid effect of substrate edges on antenna performance, you should choose length and width of substrate equal to 3 times length and width of the patch antenna respectively.
Ive seen substrates that are very slightly larger than the patch, in commercial antennas, no big deal. Its something you can easily simulate though, it does not bother that much the antenna performance (Actually the smaller ground plane will likely decrease the gain since less energy will be scattered in the broadside direction).
As for the port if its waveport as long it computes the feed line characteristic impedance correctly its alright. But its always safer to add a N/SMA connector to your model, because of its size and volume it can influence the antenna radiation pattern.
If you are talking about a single patch antenna, then choosing substrate lengths and widths on the order of 3 times the substrate thickness is the general rule. If you are talking about a patch antenna array then these dimensions begin to induce resonances which you can easily model.
This is a very interesting question with a lots of possible answer.
The performance of microctrip antenna improves to a certain extent when when we increased the height of the substrate to a certain saturation point but it may also produce unwanted result of cross polarization. Moreover there are so other relation which are based on height to width ratio e.i. for h/W>1 and h/W