<?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>4150 - Disclosure - Contingencies and Guarantees (Details)</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption>In Millions, unless otherwise specified</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>$</CurrencySymbol><contextRef><ContextID>D2013Q2YTD_InsuranceRelatedAssessmentsMember</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000727892</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><MultiplyMeasures><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure></MultiplyMeasures><NumeratorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></NumeratorMeasure><DenominatorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" 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>$</CurrencySymbol><contextRef><ContextID>D2012_InsuranceRelatedAssessmentsMember</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000727892</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2012-12-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><MultiplyMeasures><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure></MultiplyMeasures><NumeratorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></NumeratorMeasure><DenominatorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="CalendarSupplement" Id="0" Label="12 Months Ended" /><Label Key="Calendar" Id="1" Label="Dec. 31, 2012" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</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>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>true</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>D2013Q2YTD_InsuranceRelatedAssessmentsMember</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000727892</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments><anyType xsi:type="Segment"><IsDefaultForEntity>false</IsDefaultForEntity><Name /><IsFromEntityGroup>false</IsFromEntityGroup><ValueName>Future guaranty fund assessments</ValueName><ValueType>us-gaap_LossContingenciesByNatureOfContingencyAxis</ValueType><Namespace>xbrldi</Namespace><Schema>http://xbrl.org/2006/xbrldi</Schema><DimensionInfo><Id>us-gaap_InsuranceRelatedAssessmentsMember</Id><dimensionId>us-gaap_LossContingenciesByNatureOfContingencyAxis</dimensionId><type>explicitMember</type></DimensionInfo></anyType></Segments><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace><MeasureDescription /><MeasureType /></StandardMeasure><MultiplyMeasures><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure><Measure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></Measure></MultiplyMeasures><NumeratorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></NumeratorMeasure><DenominatorMeasure><MeasureSchema /><MeasureValue /><MeasureNamespace /><MeasureDescription /><MeasureType /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Key="Calendar" Id="1" Label="1/1/2013 - 6/30/2013" /></Labels></OriginalInstanceReportColumn><ElementDataType>na</ElementDataType><SimpleDataType>na</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Future guaranty fund assessments</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>us-gaap_LossContingenciesLineItems</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>terseLabel</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>Commitments and Contingencies</Label></Row><Row FlagID="0"><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_LossContingencyUndiscountedAmountOfInsuranceRelatedAssessmentLiability</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>credit</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>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD_InsuranceRelatedAssessmentsMember" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>22000000</NumericAmount><RoundedNumericAmount>22</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="D2012_InsuranceRelatedAssessmentsMember" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>26000000</NumericAmount><RoundedNumericAmount>26</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>The liability as of the balance sheet date representing required funding mandated by statute or regulatory authority that is related directly or indirectly to underwriting activities, including pools for self-insurance and excluding premium taxes and income taxes. The funds derived from the assessments generally enable a government guarantor to pay insurance claims in the event that the underwriting insurer is insolvent or otherwise unable to meet its payment obligations.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 405

 -SubTopic 30

 -Section 15

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=9154593&amp;loc=d3e23169-109297



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 405

 -SubTopic 30

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6392405&amp;loc=d3e24119-109301



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

 -Publisher AICPA

 -Name Statement of Position (SOP)

 -Number 97-3

 -Paragraph 27

 -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.



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Liability related to guaranty fund assessments</Label></Row><Row FlagID="0"><Id>4</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_LossContingencyAccrualInsuranceRelatedAssessmentPremiumTaxOffset</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>debit</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_InsuranceRelatedAssessmentsMember" UnitID="USD"><Id>1</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>17000000</NumericAmount><RoundedNumericAmount>17</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell><Cell FlagID="0" ContextID="I2012_InsuranceRelatedAssessmentsMember" UnitID="USD"><Id>2</Id><IsNumeric>true</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>19000000</NumericAmount><RoundedNumericAmount>19</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode>USD</CurrencyCode><CurrencySymbol>$</CurrencySymbol><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>true</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:monetaryItemType</ElementDataType><SimpleDataType>monetary</SimpleDataType><ElementDefenition>The amount of insurance-related assessment liability that is expected to be recovered through a premium tax offset based on current laws applied to in-force policies.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 405

 -SubTopic 30

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6392405&amp;loc=d3e24119-109301



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

 -Publisher AICPA

 -Name Statement of Position (SOP)

 -Number 97-3

 -Paragraph 22, 27

 -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.



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>2</UnitID><Label>Premium tax asset</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Contingencies and Guarantees (Details) (Future guaranty fund assessments, USD $)</ReportName><MonetaryRoundingLevel>Millions</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.riversource.com/role/DisclosureContingenciesAndGuaranteesDetails</RoleURI><NumberOfCols>2</NumberOfCols><NumberOfRows>4</NumberOfRows></InstanceReport>
