Gauss meter?

[abstruse1]

Designing and building transformers, one has to avoid going beyond the magnetic saturation point of the core. Can this be measured with a probe type Gauss meter?

It may be that magnetic saturation is greatest underneath the windings. But a probe would have to be placed on the outer surface of the winding or next to an exposed portion of the core.

[Twospoons]

It would be easier to check for saturation with  an oscilloscope measuring the winding current. Applying a constant voltage to one of the windings should result in a linear rise in current until you hit saturation, at which point you would see a sharp rise. 

I doubt you could put a gauss probe where it needs to go.
 

[klugesmith]

Yes, what twospoons said.. You can't measure the B value inside a solid core,  with a probe outside the core or in a cavity.  B can be determined accurately from measurements on any winding with known N, and knowledge of core area. I think some ferrite core applications are limited to Bmax much less than saturation, because of core loss proportional to frequency and B squared.

[edit] The question in OP is about onset of saturation.   It's not sufficient to know B without also knowing core material properties.
You care about the current (or volt-seconds product) at which induced voltage stops being proportional to dI/dt. 
Twospoons suggested a good way: apply constant voltage with a limited pulse width, and monitor current with an oscilloscope.   Current ramp becomes much steeper as you approach saturation, as long as resistive drop I * R is small compared to the applied voltage.

It's much easier at mains frequencies.  Primary AC voltage is ramped up with a variac.    Primary current is monitored with a multimeter or oscilloscope; it increases rapidly and has distorted "peaky" waveform when you approach core saturation.

[abstruse1]

If I measure saturation via oscilloscope or other such method, while transformer is not connected in circuit and operating, can I extrapolate the evidence from the scope to its real operating situation?

[klugesmith]

Sure you can.   

For a fixed frequency, volts is volts whether the transformer is in real operation or not.

More generally, what matters is the number of volt-seconds in a winding, in a positive or negative pulse between zero-voltage points.