Weather Vane’s answer, consolation prize, is what first came to my mind. You could also say that the judges made it up to the recipient for not giving her the award she truly deserved. A consolation prize is always of lower value, but we make up for not giving someone a prize he deserved by giving him another of equal value.
An award for the second-best finisher is also a runner-up award or silver medal. An American might sometimes ironically call a person who comes in second Miss Congeniality, the title of the runner-up in the Miss America beauty pageant. Someone who always does well but never wins is “always a bridesmaid, never a bride.” Thus, a special award given to honor someone who never won the annual award is a bridesmaid award. Or, more politely, a lifetime achievement award.
In some other contexts, we would use make-up as an adjective. When a referee sees a replay, realizes he got a call wrong, and calls the next play wrong for the other team to make up for it, balance the scales, and even things out, that’s a make-up call. We don’t say that for awards, though. A “make-up award” is an award for cosmetics.
This is not a participation trophy, because everyone gets one of those. It’s also not a booby prize. Those are given out mockingly, although it is possible to accept one with grace and dignity, or at least good humor. It’s not a wooden spoon either, as that is for last place, not the person who should have won.
Other commenters have suggested, replacement trophy, and that could work. It could be confused for a new trophy commissioned to replace one that has been lost or stolen.
It’s not a well-known saying, but thinking about it, the best metaphor for this in American culture might be the Academy Award for Best Actress. The Oscars are notorious for repeatedly giving it to the actress who most people felt deserved to win the year before, when they voted to give it instead to the woman who’d deserved to win the year before that.