Help Identifiying Vintage Rolex Model Number

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can anyone help with this please.

some years ago my mother lost her 1963 Rolex cocktail watch, which my father and her parents clubbed together to buy for her, & she is trying to replace it.

the only paperwork she has is the guarantee, which identifies it as "watch no. 16/3214". I haven't been able to find anything helpful in interpreting the model number & would very much appreciate it if anyone can help.

Ideally we want to nail down the model, as we already know the year and case material. Then we'll just need to track one down !

thanks all.
 
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Could be very hard to track that down, there are hundreds of cocktail watches :\
 
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True, she has been looking for a while. But if we can identify the model then I reckon we have a better chance of getting something approximate from the 60's.