[G0HZU_JMR]

See below for a model of a 4096kHz crystal. If I add some shunt capacitance then the null on the S11 measurement will shift sideways away from the 4102.663kHz null frequency seen on the s21 measurement in red.

Slowly increasing this capacitance up to 0.25pF shifts it down by about -500Hz as shown in the blue trace below where it crosses zero degrees on the graph. Note that I've shown ang[zin3] rather than the angle of the reflection coefficient as it graphs better and is easier for the reader to see the resonance point.

I would expect a real crystal to show a similar result when measured with a VNA because it will have distributed capacitance within the overall structure. It's much harder to model this distributed capacitance but it will cause a similar effect as seen in the plot below. The resonance seen with an S11 measurement will not be at the same frequency as the null seen on the 'through' S21 measurement.