We investigate the effects of central bank liquidity and possible implicit government guarantees against default on Norwegian overnight interbank interest rates. We conduct an econometric study of these interest rates over the period 2006-2009, which includes the sharp fall in interbank trading during the financial crisis. Our findings suggest relatively lower funding costs for banks of systemic importance, particularly for banks with many and valuable linkages to other banks. Moreover, interest rates are found to depend not only on overall liquidity in the interbank market, but on its distribution among banks as well. There is also evidence of stronger effects on interest rates of systemic importance, creditworthiness and liquidity demand and supply factors during the financial crisis.