How widely accepted is the euro in Bosnia and Herzegovina?

The useful World Travel Guide (WTG) currency information for Bosnia and Herzegovina says that, yes, some Euro notes are widely accepted. In my experience, that means denominations greater than 20€ (i.e., 50€ or 100€) are more difficult to use, unless being exchanged or getting smaller value bills (e.g., in a bank). Added emphasis mine.

Currency information

Bosnia and Herzegovina Konvertibilna Marka (BAM; symbol KM) = 100 feninga. Notes are in denominations of KM200, 100, 50, 20, 10, 5 and 1 and 50 feninga. Coins are available in denominations of KM2 and 1, and 50, 20 and 10 feninga. Some Euro notes (but not coins) are widely accepted.

Credit cards
Credit cards are generally accepted in top hotels and restaurants, and some gift shops. ATMs are becoming increasingly common in cities like Sarajevo, Mostar and Banja Luka, and even smaller towns. However, an emergency supply of cash is still advisable.

ATM
ATMs are becoming increasingly common in cities like Sarajevo, Mostar and Banja Luka, and even smaller towns.

Travellers cheques
Bosnia and Herzegovina is mostly a cash-only economy and traveller's cheques are exchanged only at select banks.

Banking hours
Mon-Fri 0800-1900.

Currency restrictions
The import and export of local currency are limited to KM200,000. There are no restrictions on the import and export of foreign currencies.

Currency exchange
The Euro and US Dollar are the preferred foreign currencies. The Pound Sterling is rarely used. Some shops will accept Euro cash for payment on a 2KM = 1 Euro basis.