As a "Retail Investor"
According to the question Can I buy a share from one stock exchange and sell it to another stock exchange? on Quora, to be able to buy shares on one exchange and sell on another you need to have a Demat account with a broker who is a member of both exchanges.
If this is the case, it seems appropriate to take the most favourable price when evaluating unrealised gains as – when you come to sell – you will be able to sell on the exchange offering the best price1,2.
If you don't have the ability to trade across the two exchanges, then you should use the price from the exchange where you bought (and therefore will have to sell) the shares.
Note: the above applies to unrealised gains – the potential gain (or loss) you would make if you did sell. For realised gains (actual gain/loss), you would use whatever price you actually sold your shares at.
Disclaimer for Portfolio Managers
The original answer (above) was written from the point-of-view of a "retail investor". The assumption being that the "unrealised gains" figure is little more than a "nice to have" figure to see whether, and by how much, your investments are in potential profit (while being fully aware that nothing really matters until you actually sell).
Comments from the OP to the original answer seem to suggest that they are looking at things from more of a commercial "portfolio manager"'s point-of-view, e.g.:
Many portfolios nowadays pay management fee based on whether Performance (and, or Performance History) is above or below a particular agreed upon tiers.
[...] cherry picking the highest closing prices of the two exchanges leads to unpleasantness.
Are there guidelines from the market regulator on how portfolio values should be presented to investors when same securities are traded at multiple exchanges leading to multiple closing prices?
From that point-of-view, the main answer is probably too simplistic. Yes, there very probably are regulations about how potential gains are to be reported and about "cherry-picking" prices from different exchanges. Contracts with clients (and the fees they pay) may well hinge on fractional percentage points. This answer is not aimed at such an audience.
1 I've no idea whether "cross-exchange trading" attracts higher brokerage fees or not: if it does, then you will have to factor that into any calculation of unrealised gain.
2 In practice, any price difference between the two exchanges is likely to be short-lived. As soon as one or both exchanges open, the gap is likely to disappear as market forces bring the prices back into line.