I have a 60 watt/120v clip-on lamp. What is the highest wattage of compact fluorescent bulb can I safely use in this lamp?

By the way, I mean actual watts on the fluorescent bulb, not replacement-watts. :)

You can use any bulb that draws 60 watts or less.
A 13 watt cfl puts off equivalent light to a 60 watt incandescent, but only draws 13 watts.
A 26 watt dfl puts off equivalent light to a 100 watt incandescent, but only draws 26 watts. This will be more than enough light for a clip on lamp.

Yes, the lamp is only concerned with power (number of watts), the critical issue being the intensity of the current or ampacity (watt = volt times ampere in your case 0.5). The illuminance or luminous emittance (number of lux) doesn’t really matter.