Hi Stacey,

Thanks for the question. This is a really difficult size/depth…however, hopefully, the suggestions below will help.

There are a lot of countertop microwaves that have a width of just over 12 inches (under 13 inches), but then you also have to consider the cord which typically protrudes out the back of the microwave. Typically, however, the “feet” sit back from the edge of the microwave so if you do not mind a bit of an “overhang” most of the models suggested below should fit.

We have listed some options below that you can find on Amazon.

Daewoo KOR-7LREM Retro Countertop Microwave Oven 0.7 Cu. Ft
Depth 12.7 in. inches
https://www.amazon.com/Daewoo-KOR-7LREM-Retro-Countertop-Microwave/dp/B01EZB7D2M/ref=as_li_ss_tl?ie=UTF8&linkCode=ll1&tag=gands20-20&linkId=454485a4697f99fdd380b6d9488af86f

Frigidaire FFCM0724LW
Depth 12 7/8 inches
https://www.amazon.com/Frigidaire-FFCM0724LW-700-watt-Countertop-Microwave/dp/B003VV5PNW/ref=as_li_ss_tl?ie=UTF8&qid=1531770784&sr=8-1&keywords=Frigidaire+FFCM0724LW&linkCode=ll1&tag=gands20-20&linkId=7c065e4e60eaaad75bfa5b1a56f5424e

Counter Top Rotary Microwave Oven 0.6 Cubic Feet, 600 Watt, White, WCM660W by Westinghouse
Depth – 12.5 inches
https://www.amazon.com/Counter-Rotary-Microwave-WCM660W-Westinghouse/dp/B00BGTNY8O/ref=as_li_ss_tl?ie=UTF8&qid=1531770229&sr=8-8&keywords=0.5+cu.+ft.+Countertop+Microwave&linkCode=ll1&tag=gands20-20&linkId=de242544622dea00c9fabb1bfa8ff136

GE PEM31SFSS Profile Stainless Steel Countertop Microwave
Depth – 12 7/8 inches
https://www.amazon.com/GE-PEM31SFSS-Stainless-Countertop-Microwave/dp/B01C8582Y0/ref=as_li_ss_tl?ie=UTF8&linkCode=ll1&tag=gands20-20&linkId=23d5bd74d7450b4349420af87091dada

GE JEM3072SHSS Overall
Depth: 12 3/4″
https://www.amazon.com/GE-JEM3072SHSS-Countertop-Microwave-Stainless/dp/B00U7XFELU/ref=as_li_ss_tl?ie=UTF8&linkCode=ll1&tag=gands20-20&linkId=c4f2039280876986ddf45bb39e02e978

As an alternative you can go to Amazon and search for the following:
0.5 cu. ft. Countertop Microwave
0.6 cu. ft. Countertop Microwave
0.7 cu. ft. Countertop Microwave

Hope this helps, good luck with your search.

Kind Regards,
Lisa

Thanks in advance,
Stacey