The "EMP generator" things I've seen floating around are mere toys.
The impulse isn't anywhere near useful, whether for testing purposes (it won't conform to any particular standard) or for destructive purposes (it's weak, slow and short range).
And if you're that close to a device, you can damage it much faster with a hammer...
So, I would suggest directing consideration towards commercially useful transient generators (that are often destructive, as intended!).
That said, it's hard to beat sparks. A high voltage power supply buzzing into a spark gap is quite effective. ESD is very destructive, having a risetime of nanoseconds and a peak current in the tens of amperes. A good commercial design would start with a HV supply (adjustable, since ESD is tested at various starting voltages, for various purposes), charging a capacitor through a large resistor, and discharging the capacitor through an RLC network that delivers a characteristic waveform (it's not just a resistor, by the way, despite what the equivalent diagrams show -- that would be preposterous, as the waveform has a double-peak sort of waveform, not a simple RC discharge).
For higher energy tests, there's lightning induced surge. This is usually a modest size film capacitor (say 20uF) charged up, then dumped into an RLC network which is coupled to the load. Charged to several kV, that's a fair slug of energy, and it's delivered in mere microseconds!
There are also ringing and RF-burst tests, for various applications (mil-spec bringing some of the more unusual ones). The generators may be similar to the above examples, but with different RLC networks to shape the waveform, and different charging and switching circuits to achieve the required pulse rate.
RF-burst systems have the most promise for directed energy applications, as microwaves (for example) are easily manipulated with compact antennas, waveguides, reflectors and so on. Pulsing a commercial oven magnetron gets you a fairly clean 2.45GHz (at least a few thousand cycles worth, say, if you do a few-microsecond tone burst like old school radar sets used). Clean isn't necessarily what you want; wideband chirps, wavelets and impulses have more use, as they aren't dependent on the EUT having a lucky susceptibility or immunity (depending on which side you're working from
) at some particular frequency.
These are much more difficult to generate though, and may run into concerns about import-export law(!).
The simplest wideband impulse generator would probably be a spark gap inside a ridged horn or biconical antenna. Indeed, air sparks are amazingly high bandwidth -- In the late 1800s, J. C. Bose researched frequencies up to 60GHz using mere spark gap sources!
Tim
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