The phenomenon that can damage motors is related to how a VFD functions to "trick" a motor into thinking it is getting a lower voltage along with the change in frequency using a technique called "PWM" (Pulse Width Modulation). Essentially the motor is getting a string of high speed DC pulses that it cannot react to very fast, so the "average" voltage the motor can reactor to is manipulated by changing the width of the pulses and the width of the gaps between them. In doing this, the wires and the difference in impedance (a type of resistance for AC coils) can cause reflections of voltages that cycle back and forth between the VFD and the motor terminals, building up like ripples in a pond crossing each other, until spikes of voltage begin to exceed the insulation value of the motor winding insulation.
For the most part though, this is a bigger problem for older 460V motors, where the "normal" insulation value was 2x the peak voltage of the motor design, so a lot of older 480V motors had 1000V or maybe 1200V insulation, whereas the spikes can reach 1400V or more. With 230V motors, the motor mfrs often use the same winding insulation because it's too expensive to carry two different types, so the 230V motors end up with a higher than necessary insulation level, which helps out when using a VFD.
If the motor is "irreplaceable", you can add a filter to the output of a VFD. That filter may cost as much as the VFD itself though, so you have to REALLY want to keep that old motor.The other strategy is to get whatever life you can out of the motor you already have, then if it smokes, buy a new "Inverter Duty" motor to replace it.
The other thing to be concerned with on older motors is what's called the "turn down ratio", which is a concept that didn't exist in 1950, so you likely can't get that info. It has to do with the motor's ability to cool itself if it is a fan cooled motor. So TEFC or ODP motors that have shaft mounted fans are often at risk of overheating because when you slow down the motor, you slow down the cooling fan too. TENV motors are not an issue, but there were not a lot of TENV motors in 1950. So to be safe, assume no BETTER that a 2:1 turn down ratio on an old motor, meaning never run it below 50% speed.