Does a twisted pair cable radiate more EM radiation than non-twisted pair?
If the driver sends balanced signals using a balanced drive impedance, then each wire will have equal and opposite current and voltage, so the far-field radiation of both wires will cancel out. If the wires are twisted, then each twist will radiate EM waves of opposite polarity, and they will cancel much better in the far field. In the near field (say, 1cm away from the cable) they don't, unless there are many twists per cm. The twisting effect is only effective at a distance which is relatively large to the length of a twist.
However if the driver is unbalanced (in impedance or voltage) then some common mode component will be present on the wires, which will then act as a single wire carrying this common mode component.
This occurs with most drivers, as the two resistors, and the components inside the driver, can't match perfectly. If there is a few % mismatch then the same amount of differential signal will be converted into common mode. Thus e common mode choke can be used on the differential pair to add common mode impedance without affecting the differential signal. Adding impedance reduces common mode current, and thus reduces emissions.
For example, Ethernet uses a common mode choke and a transformer. The transformer provides isolation, but also decreases the amount of common mode current sent into the pair, which is essential for long cable runs, which make very good antennas.
Common mode emissions are the same whether the wires are twisted or not.
Replying to Dave:
Any "antenna" is just as (in)effective at transmitting as it is at receiving, so the advantages of twisting the conductors together apply in both cases.
Yes, but in this case the driver and the receiver also matter: a twisted pair driven by a single ended signal will radiate due to the common mode component, but if the impedances are balanced and the receiver is differential and has good CMRR, then it can have good immunity.
So, the "low emissions" advantages of a twisted pair only occur when properly driven. If the driving signal is single-ended, then a coax would be better. Twisted pair requires a balanced driver, or a balun transformer (ie, common mode choke).