Preheat the oven to 180C/350F/Gas 4.
Strip the rosemary sprigs of most of their leaves, leaving about 2.5cm/1in of leaves at the tip. Thread the herring fillet halves onto the rosemary skewers.
Heat the oil and butter in an ovenproof frying pan and fry the herring until coloured on all sides, about 3-5 minutes.
Add the lemon halves to the pan, transfer to the oven and roast for around 8-10 minutes. Remove from the oven and serve with the roasted lemon halves.
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