It began with DJ Nick Grimshaw interrupting his Radio 1 morning show to say, "News just in: I've swallowed something weird in my drink. So now I have to go make sure I'm OK at the hospital."

It was not as louche a declaration as it sounded. What Grimshaw had swallowed was, in fact, a bit of broken glass that turned up in his mug.

But Grimshaw's handling of the incident was a textbook example of grace under pressure, on air. He made his announcement, calmly handed over the microphone to Fearne Cotton – who finished the show – and excused himself. A little while later he tweeted: "Went to hospy, had x-rays, coughed it up, all fine now."

His approach stands in marked contrast to the reaction of 5 Live presenter Shelagh Fogarty when a mouse ran across the studio during an interview last year. She screamed and climbed up on a chair. When the mouse ran across her hand, she moved studios in mid-programme. All of which was captured on a webcam.

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The thing you have to admire most of all is Grimshaw's decision not to tough it out for the last 45 minutes of his show. Countless unwell presenters have tried to push past an upset tummy out of a sense of duty – if you type "newscaster barfs" into Google you'll get an idea of the consequences.

Radio is a more forgiving medium than live TV – a lot of things can go wrong without the listener knowing – and if he wanted Grimshaw could have done all his freaking out while a record was on. But I know enough about how I respond to a crisis to know that if I ate some glass, I'd be too worried about stabbing myself from the inside to care what 6.29m listeners thought about my high-pitched shrieking.

The only unclear thing about the incident is how the glass got into Grimshaw's mug in the first place. Apparently the BBC are investigating, but no one is suggesting that Fearne Cotton put it in there on purpose. No one is saying that at all.