I think "to grill" would be「焼く（”yaku")」. 「焼き上げる("yakiageru")」　literally means to grill something up. We also use 「焼く（”yaku")」 for to bake, to toast, to roast and sometimes to burn. A part of cooker to grill fish is called　「魚焼きグリル(sakanayakiguriru"」 We also use the word gurirusuru for to grill. Sakana wo gurirusuru basically has the same meaning as sakana wo yaku(to grill fish).