<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Settlement Assets and Obligations (Policies)</ReportName>
  <ReportLongName>0409 - Disclosure - Settlement Assets and Obligations (Policies)</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="6 Months Ended" />
        <Label Id="2" Label="Jun. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDEPS</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Pure</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>pure</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Settlement Assets and Obligations (Policies) [Abstract]</Label>
      <Level>0</Level>
      <ElementName>wu_SettlementAssetsAndObligationsPoliciesAbstract</ElementName>
      <ElementPrefix>wu</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>Settlement Assets and Obligations.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>Settlement Assets and Obligations.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Investment Policy</Label>
      <Level>1</Level>
      <ElementName>us-gaap_InvestmentPolicyTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>verboselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>
    &lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
    &lt;!-- Begin Block Tagged Accounting Policy: WU-20100630_note9_accounting_policy_table1 - us-gaap:InvestmentPolicyTextBlock--&gt;
    &lt;div style="font-family: 'Times New Roman', Times"&gt;
    &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
    &lt;/div&gt;
    &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
    Investment securities consist primarily of high-quality state
    and municipal debt obligations. The Company is required to
    maintain specific high-quality, investment grade securities and
    such investments are restricted to satisfy outstanding
    settlement obligations in accordance with applicable state and
    foreign country requirements. Western Union does not hold
    investment securities for trading purposes. All investment
    securities are classified as
    &lt;font style="white-space: nowrap"&gt;available-for-sale&lt;/font&gt;
    and recorded at fair value. Investment securities are exposed to
    market risk due to changes in interest rates and credit risk.
    Western Union regularly monitors credit risk and attempts to
    mitigate its exposure by making high-quality investments and
    through investment diversification. At June&amp;#160;30, 2010, the
    majority of the Company&amp;#8217;s investment securities had credit
    ratings of &amp;#8220;AA-&amp;#8221; or better from a major credit rating
    agency.
    &lt;/div&gt;
    &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
    &lt;/div&gt;
    &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: #ffffff"&gt;
    Unrealized gains and losses on
    &lt;font style="white-space: nowrap"&gt;available-for-sale&lt;/font&gt;
    securities are excluded from earnings and presented as a
    component of accumulated other comprehensive income or loss, net
    of related deferred taxes. Gains and losses on investments are
    calculated using the specific-identification method and are
    recognized during the period the investment is sold or when an
    investment experiences an
    &lt;font style="white-space: nowrap"&gt;other-than-temporary&lt;/font&gt;
    decline in value.
    &lt;/div&gt;
    &lt;/div&gt;
  </NonNumbericText>
          <NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
    &lt;!-- Begin Block Tagged</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>Describes an entity's accounting policies for investments in financial assets, including marketable securities (debt and equity securities with readily determinable fair values), investments accounted for under the equity method and cost method, securities borrowed and loaned, and repurchase and resale agreements. For marketable securities, the description may include the entity's accounting treatment for transfers between investment categories and how the fair values for such securities are determined. Also, for all investments, an entity may describe its policy for assessing, recognizing and measuring impairment of the investment.</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 115
 -Paragraph 7-16

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 02
 -Paragraph 2, 12
 -Article 5

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Staff Accounting Bulletin (SAB)
 -Number Topic 5
 -Section M

Reference 4: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name FASB Staff Position (FSP)
 -Number FAS115-1/124-1
 -Paragraph 7-18

Reference 5: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 107
 -Paragraph 10, 11

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
