<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>4100 - Disclosure - Fair Value of Financial Instruments (Details)</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>I2013Q2</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001018164</EntityValue><PeriodDisplayName /><PeriodType>instant</PeriodType><PeriodStartDate>2013-06-30T00:00:00</PeriodStartDate><PeriodEndDate>0001-01-01T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><MultiplyMeasures><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure></MultiplyMeasures><NumeratorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></NumeratorMeasure><DenominatorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="Calendar" Id="0" Label="Jun. 30, 2013" /></Labels></Column><Column FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>I2012</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001018164</EntityValue><PeriodDisplayName /><PeriodType>instant</PeriodType><PeriodStartDate>2012-12-31T00:00:00</PeriodStartDate><PeriodEndDate>0001-01-01T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><MultiplyMeasures><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure></MultiplyMeasures><NumeratorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></NumeratorMeasure><DenominatorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="Calendar" Id="0" Label="Dec. 31, 2012" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="" UnitID=""><Id>2</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Fair value of financial instruments</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_LongTermDebt</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>credit</BalanceType><PeriodType>instant</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>positiveTerseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="I2013Q2" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>744498000</NumericAmount><RoundedNumericAmount>744498000</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="I2012" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>696988000</NumericAmount><RoundedNumericAmount>696988000</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>Carrying amount of long-term debt, net of unamortized discount or premium, including current and noncurrent amounts. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 03

 -Paragraph 16

 -Article 7



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.22)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 944

 -SubTopic 210

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.7-03.16)

 -URI http://asc.fasb.org/extlink&amp;oid=6879938&amp;loc=d3e572229-122910



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 942

 -SubTopic 210

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.9-03.16)

 -URI http://asc.fasb.org/extlink&amp;oid=6876686&amp;loc=d3e534808-122878



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 03

 -Paragraph 16

 -Article 9



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 20, 22

 -Article 5



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Carrying value on outstanding balance of notes payable</Label></Row><Row FlagID="0"><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>0</Level><ElementName /><ElementPrefix /><IsBaseElement>true</IsBaseElement><BalanceType /><PeriodType /><IsReportTitle>false</IsReportTitle><IsSegmentTitle>true</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="" UnitID=""><Id>2</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><OriginalInstanceReportColumn FlagID="0"><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>true</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>I2013Q2_FairValueInputsLevel3Member</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001018164</EntityValue><PeriodDisplayName /><PeriodType>instant</PeriodType><PeriodStartDate>2013-06-30T00:00:00</PeriodStartDate><PeriodEndDate>0001-01-01T00:00:00</PeriodEndDate><Segments><anyType xsi:type="Segment"><IsDefaultForEntity>false</IsDefaultForEntity><Name /><IsFromEntityGroup>false</IsFromEntityGroup><ValueName>Level 3</ValueName><ValueType>us-gaap_FairValueByFairValueHierarchyLevelAxis</ValueType><Namespace>xbrldi</Namespace><Schema>http://xbrl.org/2006/xbrldi</Schema><DimensionInfo><Id>us-gaap_FairValueInputsLevel3Member</Id><dimensionId>us-gaap_FairValueByFairValueHierarchyLevelAxis</dimensionId><type>explicitMember</type></DimensionInfo></anyType></Segments><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><MultiplyMeasures><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure></MultiplyMeasures><NumeratorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></NumeratorMeasure><DenominatorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="us-gaap_FairValueByFairValueHierarchyLevelAxis:us-gaap_FairValueInputsLevel3Member" Id="0" Label="Level 3" /><Label Key="Calendar" Id="1" Label="6/30/2013" /></Labels></OriginalInstanceReportColumn><ElementDataType>na</ElementDataType><SimpleDataType>na</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Level 3</Label></Row><Row FlagID="0"><Id>4</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="" UnitID=""><Id>2</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Fair value of financial instruments</Label></Row><Row FlagID="0"><Id>5</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_NotesPayableFairValueDisclosure</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>credit</BalanceType><PeriodType>instant</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="I2013Q2_FairValueInputsLevel3Member" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>734900000</NumericAmount><RoundedNumericAmount>734900000</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="I2012_FairValueInputsLevel3Member" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>697300000</NumericAmount><RoundedNumericAmount>697300000</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>This element represents the portion of the balance sheet assertion valued at fair value by the entity whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission. This item represents notes payable as of the balance sheet date.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 19, 20, 22

 -Article 5



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 129

 -Paragraph 2, 4

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.19,20,22)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Fair value of notes payable</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Fair Value of Financial Instruments (Details) (USD $)</ReportName><MonetaryRoundingLevel>NoRounding</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.willislease.com/role/DisclosureFairValueOfFinancialInstrumentsDetails</RoleURI><NumberOfCols>2</NumberOfCols><NumberOfRows>5</NumberOfRows></InstanceReport>
