How to pick/calculate component values for a tuned amplifier centered on 13.56Mhz?
You could design two seperate  tuned      loop antennas one by one .If you dont load the tuned circuit too much by say using a high input impedance preamp like say a MPF102 JFET .This means that the Q will be high in both cases and the standard formulae for resonant frequency of a tuned circuit will work fine .I have not done any 125KHz or 13.56 MHz work but I think that any open field coil would work as a receiving antenna .A bundle of ferrite rods from dead transistor AM radios would work at 125KHz .The proposed use of N bundled rods rather than just one will reduce the number of turns needed in rough proportion .Litz wire is actually still beneficial at 125 KHz because you will need lots of turns .If you dont want to do litz then consider space winding or wave winding or bank winding or any other technique to reduce proximity effect and parasitic capacitance .Coils with low parasitic capacitance tend to have higher Q which for your application means better sensitivity and batter selectivity .The 13.58 MHz is better on solid wire because     normal litz thinks that it is solid above about 3 MHz due to its significant capacitance .You could use a ferrite rod or an air cored multi turn loop with good results .If you get the Antennas right with high Q then you have enough selectivity to differentiate these far apart signals .