Before giving my answer, let me tell you what I was looking for. I run a maths centre and I wanted a quick and easy way to make dead calls to parents to pick up their kids. Skype fitted the bill but an unreliable Internet connection using a USB modem made me think of using the computer to dial the numbers. Trying to find numbers quickly on a cell phone was just too hard - often each kid has three or four numbers (mother, father, auntie, babysitter, etc.). Finally I hit on the following solution - computer generates Dual-tone multi-frequency signaling (DTMF) - those "musical sounds" you get when you press telephone keys. The program used is Excel Pro Dialer. The numbers and names are stored in an Excel sheet. A pair of old headphones are plugged into the audio jack and one of the phones is trapped in the bottom half of a 3.25 inch floppy disk box so that is in contact with the microphone of the telephone handset. There is a small movable weight (actually a circuit breaker but any other heavy object about the same size would do) on the hook of a fairly standard speaker phone.
First I fire up Excel then I start the Excel Pro Dialer. I search for parents to call on the Excel sheet using Control+F. One I have the one I want, I lift the weight off the hook (the equivalent of lifting the phone off the hook) and move the computer cursor on to the number field next to the name. Pro Dialer generates the DTMF tones on the computer, which go down to the headphone and are picked up by the headset microphone, making the phone "dial" the number. In my case, I am satisfied with a "dead call" to parents, saving me money but telling them to pick up their kids (my ID is included because it is the phone that is calling - if if the computer initiates the process). However, on the few occasions I do want to hold a phone conversation, I just press the speaker button on the phone (which cuts off the handset).
All in all, it is a very effective set-up and does what I want it to. I admit it is pretty crude but it was dirt cheap and low-tech, which in my case are advantages rather than drawbacks. The computer is an old Toshiba I was on the verge of throwing away, I had no use for the headphones. Here are some photos to show the physical arrangement - https://www.flickr.com/photos/47575775@N02/?saved=1