Forgot to mention ringing, if you are dealing with square wave, or very short bursts of AF, say 10~20 cycles of 1kHz, ringing can be a problem. I don't know why it is an issue in some transformers but not others.
I typically place a 10k metal film resistor across both primary and secondary to inhibit ringing. These values worked for me but might need to be tweaked depending on your setup.
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Ringing can be extremely difficult to see on a standard, phosphor, scope, a DSO or storage phosphor scope might be required. And you'll probably never hear it because the ringing only lasts a cycle before rapidly fading to nothing.
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This can be a real killer for modern RF data formats,
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Oh I never meant to imply that you needed a Jensen shielded transformer, in most cases you won't, but there are ham shacks with enough magnetic field strength only a premium transformer will work and they are obscenely expensive. Hence, the "rob a bank" snark.
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A quick test, connect the transformer you plan to use to a battery operated amplifier, a cassette deck will do. Use high quality mini-coax (RG-174) with good connectors and sniff for 60Hz +harmonic hum. If you have a lot, you have a problem, now I can't tell you what a lot might be because I won't have your transformer, amplifier etc. I have the coil from a 12 or 24V DC relay that I've encased in expoxy with 5 feet of RG-174. I use it for hum surveys for friends, I have an idea what is OK and what isn't but it is far from scientific.?
Now if I had 2 30V batteries, I could use my HP AF micro to 100V meter to take actual readings, but I have no idea what type relay my coil came from, it was in a friend's junk box and I didn't pay attention to anything except the dark phillips screw holding the coil in place. It was a pain to remove. I tossed the rest of the relay in his recycle bin.
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