For microwaves and other motorized appliances, your best option in the US will be heavy duty commercial products that are typically used in food service/restaurants. You can then purchase a 2100 watt microwave instead of the 1200 watt light duty residential ones. Panasonic NE-21521 is just one example of this.
For water kettles, coffee makers, and toasters, buying European models will be your best option in the US as you probably don't want the commercial equivalent which would be overkill. I agree with the comment above to install NEMA 6-15 or 6-20 plugs instead of European equivalents to avoid insurance problems and to instead change the power cords of the appliances to hide what you did to limit liability. If you do this, make sure you include GFI protection in the circuit. The reason is that UK electronics are designed expecting the neutral to not have any voltage present and to be grounded at the service entrance, but powering it with split-phase you're taking that away from it. Both hot and neutral will now have 120 volts relative to ground. This can happen in the US too, but that's why we have polarized power plugs where the neutral side is slightly larger than the hot side.
On a side note, if the 50 Hz appliance has a clock display on it, then the time might run about 20% fast if it uses the mains frequency as the timing signal. But I've heard that a 50 Hz magnetron simply won't work on 60 Hz if you were thinking about trying it. If you purchased a VFD (variable frequency drive), then depending on the model you purchased you can get any voltage and frequency combination you want. VFDs are typically used in industrial motors as speed controls, but you can use them for whatever you want!
While Ecnerwal's answer above is technically correct about the voltage not mattering when it comes to heating faster, there is another variable that does matter: wire gauge. 12 gauge wire can carry 20 amps. V=I*R, so 120 volts is 2400 watts at 20 amps, but 230 volts is 4600 watts at 20 amps. You'll see 3000 watt 230 volt water kettles for sale in the UK, but only 1500 watt models for sale in the US. This is why UK water kettles boil water faster than US water kettles.