You can use varactors which are voltage controlled capacitors to tune the patch antennas. For applying such techniques you can see for ecample the paper in the link: Conference Paper Varactor-loaded microstrip patch antenna with frequency-tuni...
You can get other solutions by searching the web for varactor tuned patch antennas.
The result of S11 is not straightforward, you better see the impedance from Smith Chart so that you could know the desired resonant frequency is of capacitive/inductive impedance.
External tuning/matching circuit could be relatively simple, which normally consists of a single LC circuit. The value of C could be electrically tunned by using varactors.