Warren Buffett is one of the most admired investors in the world. In fact, investors' confidence in his stock-picking abilities practically knows no bounds, and many flock to his annual Berkshire Hathaway shareholder meetings in Nebraska to experience Buffett in person.

Buffett has made a name for himself as a patient investor with a long-term investment horizon, who doesn't care about the erratic fluctuations of Mr. Market. He is more than willing to sit things out when times are getting tough. And Buffett has repeatedly argued that he would be more than comfortable if the stock market shut down for 10 years or so. And why?

For two reasons. First, he invests in companies that have competitive advantages such as dominant market position, pricing power, and good management. Over time, these characteristics should translate into higher earnings and a higher company valuation.

Second, many of his investments pay dividends, which accumulate over time and can make up a large part of an investment's total value. With time on his side and no intention to sell, Buffett just doesn't need to get a market quote for his investments.

Source: Wikimedia Commons.

Companies that pay a decent dividend over time have huge value for investors during times of market volatility when capital appreciation is much less certain. Consequently, stocks that have Buffett's approval, and that provide a solid dividend yield, are of great interest to investors who want to emulate the Oracle of Omaha's success.

And here are two stocks Buffett likes which offer a solid dividend.

Verizon Communications (NYSE:VZ) is a U.S. telecommunications company with a market capitalization of nearly $200 billion, and it is a new investment in Buffett's investment portfolio in 2014.

Telecommunications companies are considered defensive investments. This is because demand for their services is relatively constant. While consumers would likely cut back on discretionary spending for restaurant visits or shopping sprees if the need arises, they are also likely to keep using phone and Internet services during weaker economic times. In economic speak, their demand is more inelastic.

Since Buffett likes to invest in companies with resilient business models that generate strong free cash flow throughout the business cycle, his investment in Verizon Communications makes a lot of sense.

Free cash flow strength is a key metric for value investors: This is the cash that theoretically can be paid to shareholders in the form of dividends and/or share repurchases, because capital expenditures have already been accounted for.

In 2013, Verizon Communications achieved a massive free cash flow of $22.2 billion, which gives the company a lot of firepower to pay shareholders, and which also backs up its 4.58% dividend yield.

While ExxonMobil (NYSE:XOM) is in an entirely different industry than Verizon, it has similar characteristics.

ExxonMobil is also a dominant force its industry, oil and gas exploration, on a variety of terms, including market capitalization. The oil and gas player has a market cap of $389 billion, and is the largest publicly listed energy company in the world. It is also more than four and a half times larger than rival ConocoPhillips (NYSE:COP), which itself is not necessarily a small company, with an equity value of $84 billion.

ExxonMobil's size also reflects its competitive free cash flow strength, a metric with which the company clearly leaves its immediate oil and gas peers in the dust.

Source: ExxonMobil Investor Presentation.

Though ExxonMobil's free cash flow has fluctuated over time, and remains vulnerable to changes in underlying oil prices and the geopolitical climate, the company is nonetheless pulling in massive amounts of cash. Cash that is used to fund its recurring, low-risk dividends.

Raking in billions of dollars in free cash flow significantly reduces investment risk and speaks volumes about a company's ability to pass cash through to shareholders. ExxonMobil's stock currently yields 3.03%, which is a solid entry yield. Investors with a long-term investment horizon could capture significant dividend value by investing in ExxonMobil and reinvesting dividends.

The advantages of investing in common stocks with solid and reliable dividends backed by strong free cash flow are available to everyone. Dividends offer significant value for investors, in terms of both income and continuity. When Mr. Market hiccups and stocks tumble as a result, income investors have at least their dividends to fall back on for some steady cash to spend.

Verizon and ExxonMobil have dominant market positions in their industries, and achieve substantial free cash flow that they funnel back to shareholders via a reliable stream of dividends.