Investors have shied away from the eastern European countries in recent months over concerns about slowing economic growth and their dependence on finance from euro zone banks.
There has also been a general decline in interest from businesses based in developed markets in buying emerging markets companies, according to the Allen & Overy M&A index.
Nonetheless, there are some signs of increased focus on the eastern European emerging markets in recent months.
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"The fundamentals of the economies matter. It matters if your current account is large, it matters if your debt is large, and it matters if your fiscal situation is stable or not. All of these issues will come more under the microscope," Reza Moghadam, director of the European department of the International Monetary Fund (IMF), told CNBC.
"Countries which have strong fundamentals, whose domestic and external balances are small, will continue to have good market access."
Concerns over the effects of the actions of the U.S. Federal Reserve and European Central Bank (ECB) on the eastern Europe economies sparked a sell-off of their bonds, along with other emerging markets, in September. Since then, the debate has moved on from lumping all the eastern European countries together to the differences between their economies and prospects.
"Differentiation is the name of the game," according to Nicholas Spiro of Spiro Sovereign Strategy.
Poland and the Czech Republic are the top picks in the region, according to BNP Paribas strategists. They argue that the Polish zloty will be the "main beneficiary" of improvements in the euro zone, and that bond yields could start to react next year as the market begins to price in expected interest rate rises in 2015.
Not everyone thinks the picture is as rosy in these countries. The Czech Republic, which is heavily dependent on euro zone exports, suffered a surprise decline in GDP growth in the third quarter. The country is "massively lagging its peers in the region, held back by domestic political uncertainty and a lack of investment and borrowing," according to Nomura economist Peter Attard Montalto
Poland's status may be threatened by government plans to nationalize part of the pension funds, Greg Konieczny, executive vice president/portfolio manager at Franklin Templeton Investment Management, the fund chaired by well-known emerging markets investor Mark Mobius, warned.
"If the government takes this decision, Poland may move a few years back in terms of attractiveness of the capital markets and the economy," he told CNBC.
Romania is "emerging as a star in the region," according to Konieczny. Its third-quarter GDP growth this year was the strongest in the EU, with a rise of 4.1 percent from the same time in 2012, compared to an EU average of 0.2 percent.
The initial public offering of Romgaz, the Romanian gas company, in London and Bucharest is a "game-changer" for the country, Konieczny said.
Hungary has come out of recession and trimmed its deficit, which has led to a marked improvement in its bond market performance, but faces mounting uncertainty over decisions made by its government on foreign currency debt.
"Government policies are completely unpredictable. There's really limited appetite (for investment)," Konieczny said.
"There hasn't been any IPO for years and nothing coming close. There are very limited choices for investment."
The need for differentiation in the region is likely to continue.
"If you're going back in to emerging markets, you choose the economies that are strong and reformed, and don't have a huge dependence on foreign capital inflows if capital gets tighter," David Roche, president and global strategist at Independent Strategy, told CNBC.