Jihei, "Nagoya", with grampus-related text. Source.
There are sixteen teams left, twelve from J1, two from J2, one from J3, and one from the Kanto University League. None of the northern clubs are left so let's follow the underdogs:
Match No. 73: Matsumoto Yamaga (J2) [0 - 2] Vissel Kobe (J1)
Match No. 75: Cerezo Osaka (J1) [1 - 0] Nagoya Grampus (J2)
Match No. 76: Tsukuba University (Kanto University League) [0 - 2] Omiya Ardija (J1)
Match No. 78: Nagano Parciero (J3) [0 - 1] Jubilo Iwata (J1)
Which current J1 clubs have never won the Emperor's Cup?
Kawasaki Frontale, Vissel Kobe, Sagan Tosu, Vegalta Sendai, Consadole Sapporo, Omiya Ardija, Albirex Niigata.
Which of those clubs are still in it this year, coming into Round Four?
Kawasaki Frontale, Vissel Kobe, Omiya Ardija.
Which current J2 clubs have won the Emperor's Cup?
Shonan Bellmare, Tokyo Verdy, JEF United Chiba, Nagoya Grampus, Kyoto Sanga.
Which of those clubs are still in it this year?
Nagoya Grampus.
Have two clubs from Kansai ever met in the final?
1953: All Kwangaku (Kwansai Gakuin University, Hyōgo Prefecture) vs Osaka Club.
Vegalta Sendai in the Emperor's Cup:
96回 R2 Vegalta Sendai 2 - 5 Grulla Morioka
95回 R2 Vegalta Sendai 3 - 2 Sendai University
R3 Vegalta Sendai 0 - 0 Omiya Ardija (Vegalta won on Penalty kicks.)
R4 Vegalta Sendai 2 - 1 Matsumoto Yamaga FC
QF Vegalta Sendai 3 - 3 Kashiwa Reysol (Reysol won on penalty kicks.)
94回 R2 Vegalta Sendai 1 - 2 Nara Club
93回 R2 Vegalta Sendai 3 - 0 Blaublitz Akita
R3 Vegalta Sendai 1 - 1 Mito HollyHock (Vegalta won on penalty kicks.)
R4 Vegalta Sendai 1 - 2 FC Tokyo
92回 R2 Vegalta Sendai 1 - 0 Sony Sendai
R3 Vegalta Sendai 1 - 2 Roasso Kumamoto
91回 R2 Vegalta Sendai 2 - 1 Sony Sendai
R3 Vegalta Sendai 3 - 1 Avispa Fukuoka
R4 Cerezo Osaka 1 - 1 Vegalta Sendai (Cerezo won on penalty kicks.)
90回 R2 Vegalta Sendai 0 - 1 Sony Sendai
89回 R2 Vegalta Sendai 1 - 0 Zweigen Kanazawa
R3 Omiya Ardija 1 - 2 Vegalta Sendai
R4 FC Tokyo 0 - 3 Vegalta Sendai
QF Vegalta Sendai 2 - 1 Kawasaki Frontale
SF Gamba Osaka 2 - 1 Vegalta Sendai
88回 R3 Vegalta Sendai 2 - 0 Giravanz Kitakyushu
R4 FC Tokyo 2 - 1 Vegalta Sendai
87回 R3 Vegalta Sendai 1 - 2 Juntendo University
86回 R3 Vegalta Sendai 1 - 0 Roasso Kumamoto
R4 Nagoya Grampus 1 - 0 Vegalta Sendai
85回 R3 Vegalta Sendai 2 - 2 Sendai University (Vegalta won on penalty kicks.)
R4 Yokohama F. Marinos 4 - 0 Vegalta Sendai
84回 R3 Vegalta Sendai 2 - 0 Sagawa Printing
R4 FC Tokyo 1 - 0 Vegalta Sendai
83回 R3 Albirex Niigata 2 - 1 Vegalta Sendai
82回 R3 Vegalta Sendai 1 - 0 Ventforet Kofu
R4 Vegalta Sendai 1 - 2 JEF United Ichihara
81回 R1 FC Primeiro 0 - 4 Vegalta Sendai
R2 Vegalta Sendai 4 - 1 FC Kyoken Kyoto
R3 Sanfrecce Hiroshima 1 - 0 Vegalta Sendai
80回 R1 Kwansei Gakuin University 2 - 1 Vegalta Sendai
79回 R1 Honda Lock SC 0 - 5 Vegalta Sendai
R2 Vegalta Sendai 1 - 2 Mito HollyHock
Prior to 1999 Vegalta Sendai were known as Brummell Sendai.
78回 R1 Nirasaki Astros 2 - 3 Brummell Sendai
R2 Brummell Sendai 2 - 1 Kansai University
R3 Yokohama Marinos 0 - 1 Brummell Sendai
R4 Sanfrecce Hiroshima 3 - 0 Brummell Sendai
77回 R1 Brummell Sendai 7 - 0 Yamaga Club
R2 Brummell Sendai 0 - 1 Juntendo University
76回 R1 Matsuyama University 0 - 11 Brummell Sendai
R2 Brummell Sendai 4 - 1 Tokai University
R3 Sanfrecce Hiroshima 2 - 0 Brummell Sendai
75回 R1 Brummell Sendai 2 - 1 JEF United Ichihara
R2 Gamba Osaka 4 - 1 Brummell Sendai
Prior to 1995 Brummell Sendai were known as Tohoku Electric Power FC.
73回 R1 Tohoku Electric Power 3 - 2 Sanyo Electric Sumoto
R2 Kashima Antlers 6 - 1 Tohoku Electric Power
Team badges, part two.
Urawa Red Diamonds were formerly known as Mitsubishi Urawa FC. When they went professional they dropped the name of their corporate sponsor Mitsubishi but kept its diamond motif. (Mitsubishi means three diamonds.) Urawa is a part of Saitama City, in Saitama Prefecture, itself part of Greater Tokyo. The team badge includes a couple of local Saitama references. The red flower is the Sakurasō primrose grown in Saitama Prefecture. Along the top of the crest is a rendering of the Hōshōkaku, the main building of the Saitama Elite Teacher Training College, where soccer was first introduced to the district.
Urawa's crosstown rivals Omiya Ardija are known as the Squirrels, and have a squirrel on their badge. The club website connects the stripes on the other side of the badge to the stripes on a squirrel's back, which would lead you think that what they're calling a squirrel is really the Siberian chipmunk.
Nagoya Grampus has an orca instead of a grampus (aka Risso's dolphin) on its badge. The name actually refers to no real sea animal but to the shachi-hoko, a mythological creature with the head of tiger and the body of a carp, reputed to have the power to cause rain, and often used as a roof ornament and a charm against fire.
Shachi-hoku, or grampus, or orca. Source.