  We derive sampling functions for estimation of quantum state fidelity with
Schr\"odinger cat-like states, which are defined as superpositions of two
coherent states with opposite amplitudes. We also provide sampling functions
for fidelity with squeezed Fock states that can approximate the cat-like states
and can be generated from Gaussian squeezed states by conditional photon
subtraction. The fidelities can be determined by averaging the sampling
functions over quadrature statistics measured by homodyne detection. The
sampling functions are designed such that they can compensate for losses and
inefficient homodyning provided that the overall efficiency exceeds certain
threshold. The fidelity with an odd coherent state and the fidelity with a
squeezed odd Fock state provide convenient witnesses of negativity of Wigner
function of the measured state. The negativity of Wigner function at the origin
of phase space is certified if any of these fidelities exceeds 0.5. Finally, we
discuss the possibility of reducing the statistical uncertainty of the fidelity
estimates by a suitable choice of the dependence of the number of quadrature
samples on the relative phase shift between local oscillator and signal beam.
