Can you call a cell phone in the microwave?

It is not coincidence that the Wi-Fi frequency corresponds to the microwave
oven frequency: on the contrary. 2.4 GHz was found to be a good trade
off between microwave penetration (lower is better), and amount of
dielectric heating (higher is better). A frequency too low would not
warm up your food, too high would only warm up the outside.
When engineers
wanted to bring this to the market, they ran into a problem: you need
a license to broadcast electromagnetic waves. As it was impossible
for everyone to study for a license, in 1947 the 2.4 GHz was made
free into a Industry, Scientific and Medical band. Now every
housewife could cook without having to be a radio amateur.

Time progressed,
internet came, and so did wireless internet. The inventors of Wi-Fi
now had the same issue: it is impossible for everyone to obtain a
radio license, so they had to choose an available ISM band. The 2.4
GHz ISM band was a good choice: it had quite a large allowed
bandwidth (thus allowing for more data rate), and it was
internationally standardized (which was necessary for transatlantic
ships to have microwave ovens). Thus, not so coincidental. See
https://en.wikipedia.org/wiki/ISM_band#History

Having that out of
the way, I do know quite sure why your Wi-Fi works, while your
telephone signal doesn’t (and it’s not what you are saying).
Shielding effectiveness always decreases with frequency, so 2.4 GHz
is definitely shielded more than 700 MHz. Note that 2.4 GHz
corresponds to 12 cm wavelength, thus the assumption that the grating
is much smaller than the wavelength is valid.

For a call, your
phone needs to reach a base station, which can be either next doors,
or maybe up to a kilometer away (or even further if you are unlucky).
The base stations are those vertical white bars which are usually
grouped in three, mostly with some white disk on top of them. The
signal, although it is transmitting much power, needs to reach your
house, and then penetrate your house, thus losing nearly all of its
power. Electromagnetic power is four times lower for every time your
distance doubles, which is the same with sound. So you can imagine
your phone having to listen to someone yelling 1 km away from your
house while it is having its ears buried in fluffy pillows. And it
needs to yell back in the pillow such that the base station can still
clearly hear it, 1 km away from the house… You get the point.

For
Wi-Fi this is different. Although the maximum power of your router is
much smaller, it is also much closer. You can imagine this as having
a conversation at normal volume with someone in the same room as you,
while you have your ears and mouth in fluffy pillows. Hard, but
doable. 

To make it a bit more technical, I have done a little
test myself. I used the Wi-Fi analyzer app on my smartphone to
measure the Received Signal Strength Indication (RSSI) of my 2.4 GHz
Wi-Fi in and outside my (old) microwave oven. Since my router is
close, my RSSI outside the oven was high (-37 dBm, 0.2 microwatts:
yes, this is considered high). Inside my microwave oven the RSSI
dropped to 68 dBm (0.2 nanowatts), which is doable for Wi-Fi. I still
had a link budget of around 10 to 20 dB left before my phone would
start malfunctioning. Thus, the shielding effectiveness of my old
microwave oven at 2.4 GHz is around 30 dB: a factor 1000. Acceptable
for when the router is close by, not so much if it is at the other
side of the house.