verliehen
awarded
Describes something that was officially given to someone as an honor, prize, or title.
Der ihm verliehene Nobelpreis würdigt seine lebenslange Forschungsarbeit.
The Nobel Prize awarded to him honors his lifelong research work.

awarded / lent
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awarded
Describes something that was officially given to someone as an honor, prize, or title.
Der ihm verliehene Nobelpreis würdigt seine lebenslange Forschungsarbeit.
The Nobel Prize awarded to him honors his lifelong research work.

'Verliehen' is the past participle of the verb 'verleihen' (to award / to lend). It is very often used like an adjective before a noun to describe it.
Der ihm verliehene Orden ist eine große Ehre.
The medal awarded to him is a great honor.
The meaning of 'verliehen' (awarded / lent) depends on the context. If it is about prizes, titles, or medals, it means 'awarded.' If it is about everyday objects like books or tools, it means 'lent.'
Der verliehene Filmpreis war der Höhepunkt des Abends.
The film prize awarded was the highlight of the evening.
In the meaning 'awarded,' 'verliehen' is often used with nouns that express an honor or recognition. Typical examples are: der verliehene Preis (the awarded prize), der verliehene Titel (the awarded title), or die verliehene Medaille (the awarded medal).
Die ihr verliehene Auszeichnung würdigt ihr soziales Engagement.
The award given to her honors her social commitment.
In the meaning 'lent,' 'verliehen' is combined with everyday objects. Common examples are: das verliehene Buch (the lent book), das verliehene Auto (the lent car), or das verliehene Spiel (the lent game).
Ich muss das verliehene Buch heute in die Bibliothek zurückbringen.
I have to return the lent book to the library today.
to assign / to forgive / to miss
'vergeben' and 'verliehen' can both be used with prizes and awards. 'vergeben' describes the action: a person or organization decides who receives something. 'verliehen' usually describes the state or result: a prize or title has officially been given to someone. With awards, both can fit, but from a different perspective: you 'vergibt einen Preis' (award a prize), and afterwards the prize is 'verliehen' (awarded). Be careful: 'verliehen' can also mean that an object has only been lent out for a period of time. For that, you normally do not use 'vergeben'.

Der verliehene Titel steht seit gestern offiziell in der Zeitung.
The awarded title has officially been in the newspaper since yesterday.
Die Jury vergibt den ersten Preis an eine junge Filmemacherin.
The jury awards first prize to a young filmmaker.