A transformer cannot change the frequency, only the voltage by the ratio of primary to secondary turns. So if you put in 60Hz, you get out 60Hz.
Side effects? Yes. A transformer, or really anything designed with electromagnetic coils to produce induction, is designed based on the expected operating frequency, because (simplified) that effects the magnetism properties. Using it at a frequency it was not designed for might result in significant changes in overall efficiency (in the case of a transformer) which affects the thermal performance. So bottom line, using a transformers designed for 50Hz on a supply that is 60Hz ends up reducing the efficieny and thereby increasing the heat in the transformer. If the transformer is significantly over sized for the load, the heat increase may be survive able, but the efficiency is still lost.
This also by the way begs the question about the rest of the system, because if you have a 50Hz transformer, it might mean the rest of the machine is designed as 50Hz and if so, motors may not work the same either. Being that there are no standard 110V 50Hz motors I know of, it might be that you have changed out the motors to 60Hz designs and are wondering if you need to also change the transformers, but you did not provide adequate details for anything other than conjecture.
"Will work for (the memory of) salami"