"by telephoning" is correct and usable in written English.
You can use it when you need to refer to communicating over the phone. For example, "I confirmed the appointment by telephoning their office."
You can only book your bike by telephoning a number that costs 10p per minute.
Reservations are necessary and may be made by telephoning the Ives Festival Artists at 792‐4270.
O.F B U Y' E RS"'; ' Arriving Buyem may.restr In this column by telephoning LACkawanna 1000.
Copies of the film may be ordered by telephoning the Housing Authority at 306-3322.
Further details are available by telephoning the agency's toll-free information number, (800) 382-HOME.
More information is available by telephoning 0870 333 1183 or by visiting English Heritage's website.
He found out her address quite easily, by telephoning the conference organisers.
The lady decided to settle the argument by telephoning the Information Bureau of the "News".
How can you tell what might happen by telephoning 1,000 people at random across the whole country?
The poll was obtained by telephoning 1,009 New York City residents between Aug. 2 and Aug. 5.
You can get a state pension forecast by telephoning the government-run Future Pension Centre on 0845 300 0168.
