I have located a microwave oven that is perfect in design and features
for my particular application. The only problem is that it's a
European model. Assuming I obtain the correct transformer to transform
the voltage down to 110/115, will the difference in cycle frequency
(50Hz Euro vs. 60Hz US) be a problem? I know that, for example, with
electric clocks, this difference causes the clock to run slow or fast,
depending. Would the performance of a microwave oven be seriously
affected? If so, is there any device which adjusts cycle frequency in
the same way that a transformer steps up or down voltage?

Sellers of transformers specifically mention microwave ovens as a type
of appliance that COULD be affected by the difference in cycles (60Hz
North America vs. 50Hz foreign).  See these links:
http://www.teleadaptusa.com/nme/order_hdulstepuptrans.htm
http://www.voltagevalet.com/converters.html#info
http://www.walkabouttravelgear.com/elect.htm

One page briefly discusses the opposite situation of using a 60hz
North American appliance at 50hz. It mentions that such use won't
damage the appliance because motors would simply run at a slower
speed. Whether cycling at a faster speed would damage the appliance is
not addressed, but certainly seems plausible.
http://www.harrisonluggage.com/converters.htm

As to the second part of your question, here's a forum where folks are
discussing converting 60hz to 50hz to use a European washer/dryer in
the United States. The consenus seems to be that such a set-up is
possible by various methods such as converting the AC @ 60hz to DC
then back to AC @ 50hz. The various methods do not seem particularly
economical, however.
http://ths.gardenweb.com/forums/load/wiring/msg0301401319847.html

 
Search terms used: 50hz 60hz european u.s. microwave
://www.google.com/search?hl=en&client=googlet&q=50hz+60hz+european+u.s.+microwave&btnG=Google+Search

Additional search terms used: 50hz 60hz european appliances
transformer
://www.google.com/search?hl=en&client=googlet&q=50hz+60hz+european+appliances+transformer&btnG=Google+Search


I hope this helps. Good luck.

Perfect info. Also, would like to add that the comment I received has
very good additional info as well.

A friendly site addressing this problem is at
http://www.kropla.com/electric.htm.
Also, International Electricity issues are clarified in reasonable
English at http://www.epanorama.net/links/wire_mains.html.

The advice that is most useful comes from sellers of transformers who
say:
*** European televisions will not receive broadcasts in North America
may not operate on the 60Hz. (cycle) power systems found in the USA.
If your television operates on 50/60 Hertz, it can be used with a
European VCR or DVD to play European tapes and disks.
***Important Information: Transformers do not convert cycles (60Hz
North America vs. 50Hz foreign), and some appliances may not operate
normally when used overseas. These include, but are not limited to:
microwave ovens, analog clocks, motorized electric typewriters,
televisions and turntables. Consult the appliance manufacturer if you
have any questions.
THIS LAST SENTENCE IS OF GREAT VALUE IN PROTECTING YOUR
APPLIANCES...CHECK WITH THE DEALER. AND LOOK AT THE LABEL ON THAT
MICROWAVE...IT MAY HAVE A DESCRIPTION THAT LOOKS LIKE THIS:    "INPUT:
    AC 100V- 240V~ 1.0A  50 / 60 Hz" WHICH INDICATES THAT THE
APPLIANCE CAN HANDLE 50 OR 60 CYCLES.

http://www.teleadaptusa.com/nme/order_hdstepupungrnd.htm

One important point not covered here is the power requirements (in
watts) for microwave ovens. They produce in terms of cooking ( radio
frequency energy) anything from 400-1000watts. In turn this amount of
power plus its coversion factor from mains power to RF power has to be
supplied by the transformer. A transformer that can supply 400 watts
is large but one for 1000 watts will be very large, both physical and
electrical! The problem here is as the transformer gets larger the
in-rush current as you plug it in also gets larger as well and that is
enough is some cases to pop the breaker on the mains circuit. More
than that these transformers consumer electrical power just doing
nothing due to internal losses so watch the elctricity bill. Always
disconnect the power form the transformer when not in use and be sure
to check the rating of the outlet you are plughging it into. If the
oven draws 4 amps on 240volts AC it will draw 8+ amps on 110v AC plus
the transformer losses. You can buy transformers for this job at
www.jameco.com

As a European who moved to the USA with all my appliances I have tried
every configuration of getting things to work! Good news is 95% of
things I brought now work. The bad news in the cost of transformers
and rewiring of the house to get a 240v feed( dryer/oven type two
phase 110v  feeds) where I needed it. All  the things that don't work
were all 50/60hz critical items including the Microwave oven. The
microwave tube in the oven pulses the RF power to cook in time with
the 50Hz main feed in my model and it tripped out on 60hz.

most of the weight in a microwave oven is the transformer. Even if the
frequency difference is not a problem (and it might be), the external
conversion transformer will weigh nearly as much, and cost at least
$US 100, so I don't think it is really feasible.

Depending on the economics of the situation, one solution would be to
use an invertor system similat to those used on boats to convert 12v
to 240v AC.  Basically they consist of a 12v motor driving a 240v
generator.  Solution - get a suitable 120V60hz motor to drive a
240v50hz generator.