Do dimmers and timers not have Amp spec?
Follow the instructions regarding amps, watts and/or VA

First, you need to know how to convert between amps and watts or VA*, and apply Power Factor. 

 VA = amps x volts
 Watts = amps x volts x PF


and volts is 120 in the US typically. For incandescent lights, PF is 1.0. 

Their power limits will be expressed in terms of one of these units, and it's up to you to do the conversions.

If you don't know PF, be very generous.  Certainly if the fixture has Edison screw-in sockets, you can't possibly know the PF. Size it by assuming some epsilon minus will stick actual incandescents in there. It's unlikely for any random CFL or LED to have worse amp draw than the incandescent it replaces! 

Respect ballast and tungsten limits

The typical device may have several limits stated in several ways.  Select the one that applies to your load, and respect it...


Tungsten rating is about inrush current. This is the surge of power some devices draw initially on startup, notably incandescent bulbs (hence the word "tungsten")**.  However, CFLs, LEDs, modern electronic ballast fluorescents and electronic power supplies also have inrush, and you must respect the tungsten rating for this. 
Ballast rating is about the inductive kick generated by magnetic inductive ballasts for HID, neon and old style fluorescent lights - generally, lights that hum.  This occurs when you shut power off to them. 
Motor rating is concerned with a little of both, as a motor starting up draws its locked-rotor amperage, and packs a rather considerable inductive kick when shut off.  Typically motor ratings are in horsepower, another conversion to do, yay... 


I would expect a dimmer to be sold on its tungsten rating.  With a timer, all bets are off.   

It is quite common to see devices with an impressive amp/watt rating, and then you see the tungsten, ballast or motor rating and it's much smaller...



Notes

* some equipment uses power irregularly, I.e. "it doesn't use the whole sine wave".  Watts is what it does use, and VA is the whole sine wave which the equipment must deliver.  The equipment cares about that!  So when considering PF, we are concerned with instantaneous max amps during the normal AC cycle.  PF does not concern itself with inrush.  

  Watts / VA = Power Factor


** An incandescent bulb, when unlit, bears a strong resemblance to a dead short.  As such, it draws many amps until it starts to warm up (which it does rather quickly, given the huge shot of amps going through it!) Once at operating temperature, it behaves in a linear (resistor-like) manner, including a perfect 1.0 PF, like a resistor.