Conventional heating compared to microwave heating of chemical reactions
Your question about the 'magic' microwave effect is one that I think most chemists who've used a microwave have asked. Anecdotally, some reactions do often just work better when carried out in a microwave. The whole debate is quite nicely summarised in this quote from a (fascinating...) book on the use of microwaves in chemical synthesis: 


  Since the early days of microwave synthesis, the observed rate accelerations and sometimes altered product distributions compared to oil-bath experiments have led to speculation on the existence of so-called “specific” or “non-thermal” microwave effects. Historically, such effects were claimed when the outcome of a synthesis performed under microwave conditions was different from that of the convention- ally heated counterpart at the same apparent temperature. Reviewing the present literature, it appears that today most scientists agree that in the majority of cases the reason for the observed rate enhancements is a purely thermal/kinetic effect, i.e., a consequence of the high reaction temperatures that can rapidly be attained when irradiating polar materials in a microwave field
  
  Source: Microwaves in Organic and Medicinal Chemistry 


Microwave radiation:



Source: Microwaves in Organic and Medicinal Chemistry 

From the table above, its clear that microwave radiation is not strong enough to cause any actual chemical change itself (other than via the temperature it creates), for microwave radiation used by common household and lab microwaves (2450 MHz, which is important as it avoids interfering with communication equipment), the energy is sufficiently low that it couldn't in theory even over-come a hydrogen bond. 

Thermal/pressure effects:

There are several reasons why the use of a microwave may be beneficial compared to a standard reflux setup in a PEG bath (or any other conventional heating method):


the microwave is able to quickly reach a given temperature, with only a short induction period. The result of this is that the reaction reaches the desired temperature quickly, rather than slowly warming from room temperature. This means that the reaction gets going immediately, which can be especially beneficial in cases where the catalyst/reagents being used aren't terribly stable (your metathesis is one such example where the catalyst can quickly degrade in solution). 
the microwave heats the solution directly and uniformly, compared to heating conveniently where the glass is being heated and in turn the glass heats the solution. 



Source: Biotage. Left image = microwave heating, right image = oil bath, both taken after 1 min of heating  


the vials used in microwave reactions are sealed (they're closed systems), which means in addition to temperature, they're able to carry out reactions under increased pressure, allowing the reaction to be heated above the boiling point of the solvent being used. 




Source: Biotage 

Overall, the easiest way to show all of this is by looking at the read-out from a microwave reaction, showing how quickly the desired temperature can be reached and how this remains constant, along with the pressure, throughout the entire reaction run:  



Non-thermal effects:

Non-thermal effects, or 'specific microwave effects' are defined as accelerations of chemical transformations in a microwave field that cannot be achieved or duplicated by conventional heating, but essentially are still thermal effects. These have been considered by many groups and indeed a wikipedia page exists discussing them, however they're difficult to show/prove experimentally. 

For solution phase organic synthesis, its generally accepted that there is no specific microwave effect. Only in solid phase systems (ionic lattices for example) is there anything to suggest something unique going on that cannot be achieved using standard heating methods alone.