How do I tune a low frequency series resonant circuit?
Your resonant circuit in your uC prototype is detuned compared to your signal generator set-up. So your 1% capacitors aren't a good match anymore.

The inductor will interact heavily with all metals (pcb material) around it and will change its inductivity. Also if your inductor gets charged up part of the magnetic field will create eddy currents in the nearby metals. This leaks energy out of your resonant circuit lowering the output voltage.

As for automatic tuning: I researched different methods over the last month for an RFID project and didn't found anything practical. 

The most promising way was using varicap diodes to do the tuning but they only work if the voltage within your resonant tank stays relative low. Otherwise the signal swing itself will detune the varicaps and you end up with a non-linear system. 

I suggest that you keep tuning your circuit by changing the capacitor until you hit the resonant frequency. If you have access to a network analyzer you can directly measure the current resonant frequency and calculate the required capacitance. That gets you close but you'll likely have to add or remove a few picofarads as the analyzer will have a detuning effect itself.

Without such measuring equipment it's harder but still doable. Change the capacitance a bit and observe the output voltage. If it goes up you've moved closer to the resonant frequency. If it drops lower the capacitor instead. With ten iterations or so you should get close to your resonant frequency.

(I'd start by removing capacitance because it's likely that your inductance went up).

Be prepared to redo this step each time you add or remove metal to your device. E.g. if you add for example batteries to your prototype expect your tuning to drift away again.