The bandwidth of transformer is determined based on insertion loss. Haven't heard of this parameter -- transformer's self-resonant frequency. Where did u see this parameter?
I don´t know if there is what you´re looking for, but when the transformer windings is performed ending not in an entire turn ( n+1/2 ), the electronic model of this transformer is equal to an ideal transformer in series with a 1-Turn inductor ( It can be proven ).
This way is possible to create a built-in inductor with no need of mode cores.
Adding a capacitor the equivalent circuit will get a natural ressonating frequency.
After reviewing the equivalent circuit of transformers, I found there are intra-/inter-winding stray capacitances. These stray capacitances will resonante with the leakage inductances or the winding inductances (at lower frequencies). This phenomenon should be the so-called transformer self-resoance.